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Triangles
RD Sharma
CBSE
Grade 10

Question:

In $\Delta ABC$, $D$ and $E$ are points on sides $AB$ and $AC$ respectively such that $DE \parallel BC$. If $AD = x, DB = x - 2, AE = x + 2$ and $EC = x - 1$, then $x$ is equal to:
(a) $4$
(b) $3$
(c) $2$
(d) $5$

Step-by-Step Solution

Key Concept: By BPT: $\dfrac{x}{x-2} = \dfrac{x+2}{x-1} \Rightarrow x(x - 1) = (x - 2)(x + 2) \Rightarrow x^2 - x = x^2 - 4 \Rightarrow -x = -4 \Rightarrow x = 4$.
$x(x - 1) = (x - 2)(x + 2) \Rightarrow x^2 - x = x^2 - 4 \Rightarrow x = 4$. [1.0 Mark]

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🎯 Official CBSE Marking Scheme:
Cross multiplying and solving $x = 4$: 1.0 Mark

Correct Answer: $4$
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