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In triangle ABC, DE || BC. If AD = $x$ , DB = $x - 2$ , AE = $x + 2$ and EC = $x - 1$ , the value of $x$ found from BPT is ____.

Class 10Basic Proportionality TheoremGeometry — Similarity

A4
B3
C5
D6

Step-by-Step Solution

\frac{x}{x - 2} = \frac{x + 2}{x - 1}

. Cross-multiply:

x (x - 1) = (x - 2) (x + 2), x^{2} - x = x^{2} - 4

, so

- x = - 4, x = 4

.

Answer: A) 4

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