In a Δ ABC, if D and E are the points on the sides AB and AC respectively such that DE || BC and if AD = x , DB = x – 2 , AE = x + 2 and EC = x – 1. then find the value of x .

5 4 3 2

4

∴ \(\frac{AD}{DB}\) = \(\frac{AE}{EC}\) ⇒ \(\frac{x}{x - 2}\) = \(\frac{x + 2}{x - 1}\) ⇒ x(x – 1) = (x + 2) (x – 2) ⇒ x2 – x = x2 – 4 ⇒ x = 4