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Mathematics · 2023 · 2 marks
CBSE 2023 · Region 1 · Set 3 · Q24
In the given figure, ABCD is a parallelogram. AE divides the line segment BD in the ratio 1: 2. If BE =1.5 cm, then find the length of BC.
In the given figure, ABCD is a parallelogram. AE divides the line segment BD in the ratio $\displaystyle 1: 2$. If $\displaystyle \mathrm{BE}=1.5 \mathrm{~cm}$, then find the length of BC .
Marking-scheme solution
\[\begin{aligned}
& \Delta \mathrm{OBE} \sim \Delta \mathrm{ODA} \\
& \Rightarrow \frac{O B}{O D}=\frac{B E}{A D} \\
& \Rightarrow \frac{1}{2}=\frac{B E}{B C}(\mathrm{AD}=\mathrm{BC}) \\
& \mathrm{BE}=1 \cdot 5 \mathrm{~cm} \Rightarrow \mathrm{BC}=3 \mathrm{~cm}
\end{aligned}
\]
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