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Triangles
RD Sharma
CBSE
Grade 10
Question:
In $\Delta ABC$, $D$ and $E$ are on $AB$ and $AC$ such that $DE \parallel BC$. If $AD : DB = 2 : 3$, then $AE : AC$ is: (a) $2 : 5$ (b) $2 : 3$ (c) $3 : 5$ (d) $3 : 2$
Step-by-Step Solution
Key Concept: $AD / AB = AD / (AD + DB) = 2 / (2 + 3) = 2 / 5$. By BPT corollary, $AE / AC = AD / AB = 2 / 5$.
$\dfrac{AE}{AC} = \dfrac{AD}{AB} = \dfrac{2}{2 + 3} = \dfrac{2}{5}$. Ratio is $2 : 5$. [1.0 Mark]
--- 🎯 Official CBSE Marking Scheme: Evaluating ratio $2 : 5$: 1.0 Mark
Correct Answer:$2 : 5$
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