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 .
Answer & explanation
Correct answer: option 2
∴ \(\frac{AD}{DB}\) = \(\frac{AE}{EC}\)
⇒ \(\frac{x}{x - 2}\) = \(\frac{x + 2}{x - 1}\)
⇒ x(x – 1) = (x + 2) (x – 2)
⇒ x2 – x = x2 – 4
⇒ x = 4