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Area of Composite Figures
Question 1 of 101
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=2:1$ and $AE:CE=1:3$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:2 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 1:3=2:6 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 1:2:6$.
Yay! Your are right.
Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:2 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 1:3=2:6 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 1:2:6$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=2:1$ and $AE:CE=1:3$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Yay! Your are right.
Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:2 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 1:3 = 2 : 6 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 1:2:6$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=2:1$ and $AE:CE=1:4$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:2 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 1:4 = 2 : 8 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 1:2:8$.
Yay! Your are right.
Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:2 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 1:4 = 2 : 8 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 1:2:8$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=2:1$ and $AE:CE=1:5$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:2 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 1:5 = 2 : 10 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 1:2:10$.
Yay! Your are right.
Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:2 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 1:5 = 2 : 10 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 1:2:10$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=2:1$ and $AE:CE=1:6$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:2 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 1:6 = 2 : 12 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 1:2:12$.
Yay! Your are right.
Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:2 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 1:6 = 2 : 12 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 1:2:12$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=2:1$ and $AE:CE=1:7$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:2 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 1:7 = 2 : 14 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 1:2:14$.
Yay! Your are right.
Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:2 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 1:7 = 2 : 14 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 1:2:14$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=2:1$ and $AE:CE=1:8$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:2 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 1:8 = 2 : 16 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 1:2:16$.
Yay! Your are right.
Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:2 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 1:8 = 2 : 16 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 1:2:16$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=2:1$ and $AE:CE=1:9$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:2 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 1:9 = 2 : 18 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 1:2:18$.
Yay! Your are right.
Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:2 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 1:9 = 2 : 18 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 1:2:18$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=2:1$ and $AE:CE=2:3$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:2 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 2:3 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 1:2:3$.
Yay! Your are right.
Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:2 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 2:3 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 1:2:3$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=2:1$ and $AE:CE=2:5$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Sorry. Please check the correct answer below.
Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:2 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 2:5 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 1:2:5$.
Yay! Your are right.
Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:2 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 2:5 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 1:2:5$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=2:1$ and $AE:CE=2:6$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Sorry. Please check the correct answer below.
Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:2 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 2:6 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 1:2:6$.
Yay! Your are right.
Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:2 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 2:6 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 1:2:6$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=2:1$ and $AE:CE=2:7$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:2 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 2:7 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 1:2:7$.
Yay! Your are right.
Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:2 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 2:7 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 1:2:7$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=2:1$ and $AE:CE=2:8$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Sorry. Please check the correct answer below.
Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:2 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 2:8 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 1:2:8$.
Yay! Your are right.
Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:2 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 2:8 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 1:2:8$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=2:1$ and $AE:CE=2:9$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Sorry. Please check the correct answer below.
Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:2 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 2:9 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 1:2:9$.
Yay! Your are right.
Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:2 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 2:9 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 1:2:9$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=2:1$ and $AE:CE=3:4$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:2 = 3 : 6 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 3:4 = 6 : 8 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 3:6:8$.
Yay! Your are right.
Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:2 = 3 : 6 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 3:4 = 6 : 8 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 3:6:8$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=2:1$ and $AE:CE=3:5$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:2 = 3 : 6 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 3:5 = 6 : 10 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 3:6:10$.
Yay! Your are right.
Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:2 = 3 : 6 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 3:5 = 6 : 10 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 3:6:10$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=2:1$ and $AE:CE=3:7$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:2 = 3 : 6 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 3:7 = 6 : 14 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 3:6:14$.
Yay! Your are right.
Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:2 = 3 : 6 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 3:7 = 6 : 14 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 3:6:14$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=2:1$ and $AE:CE=3:8$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:2 = 3 : 6 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 3:8 = 6 : 16 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 3:6:16$.
Yay! Your are right.
Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:2 = 3 : 6 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 3:8 = 6 : 16 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 3:6:16$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=2:1$ and $AE:CE=3:9$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:2 = 3 : 6 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 3:9 = 6 : 18 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 3:6:18$.
Yay! Your are right.
Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:2 = 3 : 6 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 3:9 = 6 : 18 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 3:6:18$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=2:1$ and $AE:CE=4:5$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:2 = 2 : 4 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 4:5 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 2:4:5$.
Yay! Your are right.
Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:2 = 2 : 4 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 4:5 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 2:4:5$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=2:1$ and $AE:CE=4:6$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:2 = 2 : 4 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 4:6 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 2:4:6$.
Yay! Your are right.
Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:2 = 2 : 4 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 4:6 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 2:4:6$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=2:1$ and $AE:CE=4:7$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:2 = 2 : 4 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 4:7 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 2:4:7$.
Yay! Your are right.
Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:2 = 2 : 4 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 4:7 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 2:4:7$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=2:1$ and $AE:CE=4:9$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:2 = 2 : 4 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 4:9 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 2:4:9$.
Yay! Your are right.
Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:2 = 2 : 4 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 4:9 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 2:4:9$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=2:1$ and $AE:CE=5:6$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:2 = 5 : 10 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 5:6 = 10 : 12 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 5:10:12$.
Yay! Your are right.
Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:2 = 5 : 10 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 5:6 = 10 : 12 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 5:10:12$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=2:1$ and $AE:CE=5:7$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:2 = 5 : 10 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 5:7 = 10 : 14 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 5:10:14$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:2 = 5 : 10 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 5:7 = 10 : 14 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 5:10:14$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=2:1$ and $AE:CE=5:8$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:2 = 5 : 10 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 5:8 = 10 : 16 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 5:10:16$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:2 = 5 : 10 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 5:8 = 10 : 16 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 5:10:16$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=2:1$ and $AE:CE=5:9$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:2 = 5 : 10 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 5:9 = 10 : 18 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 5:10:18$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:2 = 5 : 10 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 5:9 = 10 : 18 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 5:10:18$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=2:1$ and $AE:CE=6:7$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:2 = 3 : 6 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 6:7 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 3:6:7$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:2 = 3 : 6 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 6:7 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 3:6:7$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=2:1$ and $AE:CE=6:8$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:2 = 3 : 6 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 6:8 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 3:6:8$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:2 = 3 : 6 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 6:8 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 3:6:8$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=2:1$ and $AE:CE=6:9$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:2 = 3 : 6 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 6:9 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 3:6:9$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:2 = 3 : 6 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 6:9 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 3:6:9$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=2:1$ and $AE:CE=7:8$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:2 = 7 : 14 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 7:8 = 14 : 16 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 7:14:16$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:2 = 7 : 14 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 7:8 = 14 : 16 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 7:14:16$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=2:1$ and $AE:CE=7:9$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:2 = 7 : 14 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 7:9 = 14 : 18 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 7:14:18$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:2 = 7 : 14 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 7:9 = 14 : 18 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 7:14:18$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=2:1$ and $AE:CE=8:9$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:2 = 4 : 8 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 8:9 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 4:8:9$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:2 = 4 : 8 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 8:9 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 4:8:9$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=3:1$ and $AE:CE=1:2$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:3 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 1:2 = 3 : 6 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 1:3:6$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:3 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 1:2 = 3 : 6 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 1:3:6$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=3:1$ and $AE:CE=1:4$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:3 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 1:4 = 3 : 12 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 1:3:12$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:3 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 1:4 = 3 : 12 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 1:3:12$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=3:1$ and $AE:CE=1:5$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:3 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 1:5 = 3 : 15 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 1:3:15$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:3 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 1:5 = 3 : 15 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 1:3:15$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=3:1$ and $AE:CE=1:6$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:3 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 1:6 = 3 : 18 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 1:3:18$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:3 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 1:6 = 3 : 18 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 1:3:18$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=3:1$ and $AE:CE=1:7$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:3 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 1:7 = 3 : 21 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 1:3:21$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:3 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 1:7 = 3 : 21 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 1:3:21$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=3:1$ and $AE:CE=1:8$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:3 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 1:8 = 3 : 24 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 1:3:24$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:3 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 1:8 = 3 : 24 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 1:3:24$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=3:1$ and $AE:CE=1:9$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:3 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 1:9 = 3 : 27 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 1:3:27$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:3 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 1:9 = 3 : 27 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 1:3:27$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=3:1$ and $AE:CE=2:3$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:3 = 2 : 6 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 2:3 = 6 : 9 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 2:6:9$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:3 = 2 : 6 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 2:3 = 6 : 9 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 2:6:9$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=3:1$ and $AE:CE=2:4$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:3 = 2 : 6 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 2:4 = 6 : 12 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 2:6:12$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:3 = 2 : 6 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 2:4 = 6 : 12 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 2:6:12$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=3:1$ and $AE:CE=2:5$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:3 = 2 : 6 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 2:5 = 6 : 15 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 2:6:15$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:3 = 2 : 6 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 2:5 = 6 : 15 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 2:6:15$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=3:1$ and $AE:CE=2:7$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:3 = 2 : 6 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 2:7 = 6 : 21 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 2:6:21$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:3 = 2 : 6 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 2:7 = 6 : 21 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 2:6:21$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=3:1$ and $AE:CE=2:8$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:3 = 2 : 6 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 2:8 = 6 : 24 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 2:6:24$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:3 = 2 : 6 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 2:8 = 6 : 24 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 2:6:24$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=3:1$ and $AE:CE=2:9$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:3 = 2 : 6 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 2:9 = 6 : 27 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 2:6:27$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:3 = 2 : 6 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 2:9 = 6 : 27 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 2:6:27$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=3:1$ and $AE:CE=3:4$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:3 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 3:4 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 1:3:4$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:3 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 3:4 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 1:3:4$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=3:1$ and $AE:CE=3:5$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:3 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 3:5 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 1:3:5$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:3 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 3:5 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 1:3:5$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=3:1$ and $AE:CE=3:6$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:3 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 3:6 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 1:3:6$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:3 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 3:6 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 1:3:6$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=3:1$ and $AE:CE=3:7$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:3 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 3:7 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 1:3:7$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:3 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 3:7 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 1:3:7$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=3:1$ and $AE:CE=3:8$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:3 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 3:8 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 1:3:8$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:3 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 3:8 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 1:3:8$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=3:1$ and $AE:CE=4:5$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:3 = 4 : 12 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 4:5 = 12 : 15 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 4:12:15$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:3 = 4 : 12 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 4:5 = 12 : 15 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 4:12:15$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=3:1$ and $AE:CE=4:6$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:3 = 4 : 12 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 4:6 = 12 : 18 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 4:12:18$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:3 = 4 : 12 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 4:6 = 12 : 18 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 4:12:18$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=3:1$ and $AE:CE=4:7$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:3 = 4 : 12 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 4:7 = 12 : 21 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 4:12:21$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:3 = 4 : 12 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 4:7 = 12 : 21 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 4:12:21$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=3:1$ and $AE:CE=4:8$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:3 = 4 : 12 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 4:8 = 12 : 24 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 4:12:24$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:3 = 4 : 12 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 4:8 = 12 : 24 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 4:12:24$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=3:1$ and $AE:CE=4:9$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:3 = 4 : 12 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 4:9 = 12 : 27 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 4:12:27$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:3 = 4 : 12 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 4:9 = 12 : 27 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 4:12:27$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=3:1$ and $AE:CE=5:6$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:3 = 5 : 15 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 5:6 = 15 : 18 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 5:15:18$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:3 = 5 : 15 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 5:6 = 15 : 18 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 5:15:18$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=3:1$ and $AE:CE=5:7$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:3 = 5 : 15 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 5:7 = 15 : 21 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 5:15:21$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:3 = 5 : 15 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 5:7 = 15 : 21 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 5:15:21$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=3:1$ and $AE:CE=5:8$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:3 = 5 : 15 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 5:8 = 15 : 24 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 5:15:24$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:3 = 5 : 15 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 5:8 = 15 : 24 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 5:15:24$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=3:1$ and $AE:CE=5:9$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:3 = 5 : 15 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 5:9 = 15 : 27 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 5:15:27$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:3 = 5 : 15 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 5:9 = 15 : 27 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 5:15:27$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=3:1$ and $AE:CE=6:7$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:3 = 2 : 6 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 6:7 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 2:6:7$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:3 = 2 : 6 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 6:7 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 2:6:7$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=3:1$ and $AE:CE=6:8$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:3 = 2 : 6 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 6:8 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 2:6:8$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:3 = 2 : 6 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 6:8 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 2:6:8$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=3:1$ and $AE:CE=6:9$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:3 = 2 : 6 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 6:9 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 2:6:9$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:3 = 2 : 6 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 6:9 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 2:6:9$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=3:1$ and $AE:CE=7:8$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:3 = 7 : 21 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 7:8 = 21 : 24 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 7:21:24$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:3 = 7 : 21 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 7:8 = 21 : 24 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 7:21:24$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=3:1$ and $AE:CE=7:9$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:3 = 7 : 21 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 7:9 = 21 : 27 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 7:21:27$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:3 = 7 : 21 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 7:9 = 21 : 27 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 7:21:27$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=3:1$ and $AE:CE=8:9$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:3 = 8 : 24 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 8:9 = 24 : 27 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 8:24:27$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:3 = 8 : 24 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 8:9 = 24 : 27 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 8:24:27$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=3:2$ and $AE:CE=1:2$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 2:3 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 1:2 = 3 : 6 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 2:3:6$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 2:3 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 1:2 = 3 : 6 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 2:3:6$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=3:2$ and $AE:CE=1:3$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 2:3 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 1:3 = 3 : 9 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 2:3:9$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 2:3 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 1:3 = 3 : 9 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 2:3:9$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=3:2$ and $AE:CE=1:4$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 2:3 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 1:4 = 3 : 12 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 2:3:12$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 2:3 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 1:4 = 3 : 12 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 2:3:12$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=3:2$ and $AE:CE=1:5$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 2:3 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 1:5 = 3 : 15 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 2:3:15$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 2:3 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 1:5 = 3 : 15 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 2:3:15$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=3:2$ and $AE:CE=1:6$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 2:3 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 1:6 = 3 : 18 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 2:3:18$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 2:3 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 1:6 = 3 : 18 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 2:3:18$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=3:2$ and $AE:CE=1:7$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 2:3 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 1:7 = 3 : 21 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 2:3:21$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 2:3 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 1:7 = 3 : 21 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 2:3:21$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=3:2$ and $AE:CE=1:8$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 2:3 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 1:8 = 3 : 24 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 2:3:24$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 2:3 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 1:8 = 3 : 24 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 2:3:24$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=3:2$ and $AE:CE=1:9$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 2:3 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 1:9 = 3 : 27 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 2:3:27$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 2:3 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 1:9 = 3 : 27 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 2:3:27$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=3:2$ and $AE:CE=2:4$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 2:3 = 4 : 6 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 2:4 = 6 : 12 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 4:6:12$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 2:3 = 4 : 6 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 2:4 = 6 : 12 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 4:6:12$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=3:2$ and $AE:CE=2:5$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 2:3 = 4 : 6 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 2:5 = 6 : 15 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 4:6:15$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 2:3 = 4 : 6 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 2:5 = 6 : 15 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 4:6:15$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=3:2$ and $AE:CE=2:6$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 2:3 = 4 : 6 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 2:6 = 6 : 18 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 4:6:18$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 2:3 = 4 : 6 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 2:6 = 6 : 18 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 4:6:18$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=3:2$ and $AE:CE=2:7$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 2:3 = 4 : 6 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 2:7 = 6 : 21 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 4:6:21$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 2:3 = 4 : 6 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 2:7 = 6 : 21 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 4:6:21$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=3:2$ and $AE:CE=2:8$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 2:3 = 4 : 6 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 2:8 = 6 : 24 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 4:6:24$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 2:3 = 4 : 6 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 2:8 = 6 : 24 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 4:6:24$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=3:2$ and $AE:CE=2:9$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 2:3 = 4 : 6 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 2:9 = 6 : 27 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 4:6:27$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 2:3 = 4 : 6 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 2:9 = 6 : 27 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 4:6:27$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=3:2$ and $AE:CE=3:4$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 2:3 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 3:4 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 2:3:4$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 2:3 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 3:4 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 2:3:4$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=3:2$ and $AE:CE=3:5$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 2:3 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 3:5 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 2:3:5$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 2:3 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 3:5 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 2:3:5$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=3:2$ and $AE:CE=3:6$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 2:3 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 3:6 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 2:3:6$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 2:3 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 3:6 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 2:3:6$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=3:2$ and $AE:CE=3:7$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 2:3 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 3:7 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 2:3:7$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 2:3 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 3:7 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 2:3:7$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=3:2$ and $AE:CE=3:8$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 2:3 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 3:8 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 2:3:8$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 2:3 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 3:8 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 2:3:8$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=3:2$ and $AE:CE=3:9$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 2:3 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 3:9 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 2:3:9$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 2:3 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 3:9 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 2:3:9$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=3:2$ and $AE:CE=4:5$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 2:3 = 8 : 12 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 4:5 = 12 : 15 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 8:12:15$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 2:3 = 8 : 12 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 4:5 = 12 : 15 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 8:12:15$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=3:2$ and $AE:CE=4:7$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 2:3 = 8 : 12 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 4:7 = 12 : 21 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 8:12:21$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 2:3 = 8 : 12 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 4:7 = 12 : 21 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 8:12:21$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=3:2$ and $AE:CE=4:8$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 2:3 = 8 : 12 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 4:8 = 12 : 24 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 8:12:24$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 2:3 = 8 : 12 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 4:8 = 12 : 24 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 8:12:24$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=3:2$ and $AE:CE=4:9$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 2:3 = 8 : 12 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 4:9 = 12 : 27 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 8:12:27$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 2:3 = 8 : 12 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 4:9 = 12 : 27 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 8:12:27$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=3:2$ and $AE:CE=5:6$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 2:3 = 10 : 15 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 5:6 = 15 : 18 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 10:15:18$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 2:3 = 10 : 15 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 5:6 = 15 : 18 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 10:15:18$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=3:2$ and $AE:CE=5:7$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 2:3 = 10 : 15 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 5:7 = 15 : 21 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 10:15:21$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 2:3 = 10 : 15 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 5:7 = 15 : 21 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 10:15:21$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=3:2$ and $AE:CE=5:8$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 2:3 = 10 : 15 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 5:8 = 15 : 24 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 10:15:24$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 2:3 = 10 : 15 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 5:8 = 15 : 24 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 10:15:24$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=3:2$ and $AE:CE=5:9$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 2:3 = 10 : 15 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 5:9 = 15 : 27 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 10:15:27$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 2:3 = 10 : 15 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 5:9 = 15 : 27 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 10:15:27$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=3:2$ and $AE:CE=6:7$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 2:3 = 4 : 6 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 6:7 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 4:6:7$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 2:3 = 4 : 6 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 6:7 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 4:6:7$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=3:2$ and $AE:CE=6:8$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 2:3 = 4 : 6 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 6:8 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 4:6:8$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 2:3 = 4 : 6 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 6:8 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 4:6:8$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=3:2$ and $AE:CE=7:8$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 2:3 = 14 : 21 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 7:8 = 21 : 24 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 14:21:24$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 2:3 = 14 : 21 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 7:8 = 21 : 24 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 14:21:24$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=3:2$ and $AE:CE=7:9$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 2:3 = 14 : 21 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 7:9 = 21 : 27 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 14:21:27$.
Yay! Your are right.
Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 2:3 = 14 : 21 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 7:9 = 21 : 27 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 14:21:27$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=3:2$ and $AE:CE=8:9$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 2:3 = 16 : 24 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 8:9 = 24 : 27 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 16:24:27$.
Yay! Your are right.
Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 2:3 = 16 : 24 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 8:9 = 24 : 27 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 16:24:27$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=4:1$ and $AE:CE=1:2$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:4 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 1:2 = 4 : 8 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 1:4:8$.
Yay! Your are right.
Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:4 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 1:2 = 4 : 8 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 1:4:8$.
Lines $AC$ and $BD$ divide the quadrilateral $ABCD$ into 4 triangles of different areas. Given that $BE:DE=4:1$ and $AE:CE=1:3$, find the ratio of the areas $\triangle ADE: \triangle BCE$.
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Sorry. Please check the correct answer below.
Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:4 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 1:3 = 4 : 12 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 1:4:12$.
Yay! Your are right.
Since $\triangle ABE$ and $\triangle ADE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ADE: \triangle ABE = 1:4 \end{equation*} Since $\triangle ABE$ and $\triangle BCE$ share the same height, then \begin{equation*} \text{Ratio of areas }\triangle ABE: \triangle BCE = 1:3 = 4 : 12 \end{equation*} Thus, ratio of areas $\triangle ADE: \triangle ABE: \triangle BCE = 1:4:12$.
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