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Triangles
NCERT Exemplar
CBSE
Grade 10
Question:
In $\Delta ABC$, $D$ and $E$ are points on sides $AB$ and $AC$ respectively such that $DE \parallel BC$. If $AD = 2\text{ cm}, DB = 3\text{ cm}, AE = 4\text{ cm}$, then $EC$ is:
(a) $6\text{ cm}$
(b) $5\text{ cm}$
(c) $4\text{ cm}$
(d) $8\text{ cm}$
(a) $6\text{ cm}$
(b) $5\text{ cm}$
(c) $4\text{ cm}$
(d) $8\text{ cm}$
Step-by-Step Solution
Key Concept: Basic Proportionality Theorem (BPT): $\dfrac{AD}{DB} = \dfrac{AE}{EC}$.
$\dfrac{AD}{DB} = \dfrac{AE}{EC} \Rightarrow \dfrac{2}{3} = \dfrac{4}{EC}$. [0.5 Mark]
$2 EC = 12 \Rightarrow EC = 6\text{ cm}$. [0.5 Mark]
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🎯 Official CBSE Marking Scheme:
BPT ratio setup: 0.5 Mark
Calculating $EC = 6\text{ cm}$: 0.5 Mark
$2 EC = 12 \Rightarrow EC = 6\text{ cm}$. [0.5 Mark]
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🎯 Official CBSE Marking Scheme:
BPT ratio setup: 0.5 Mark
Calculating $EC = 6\text{ cm}$: 0.5 Mark
Correct Answer: $6\text{ cm}$
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