Question

In △ABC, DE || BC. AD = x, DB = x – 2, AE = x + 2 and EC = x – 1. Find the value of x.

Answer 1

Given: In △ABC, DE // BC

∴ By Basic proportionality theorem, we have 

\(\frac{AD}{DB}=\frac{AE}{EC}\)

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

⇒ x (x – 1) = (x + 2) (x – 2) 

⇒ x² – x = x² – 4 

⇒ -x = -4 

∴ x = 4