Question

D and E are points on the sides AB and AC respectively of a ΔABC such that DE || BC. Find the value of x, when AD = x cm, DB = (x – 2) cm, AE = (x + 2) cm and EC = (x – 1) cm. 

Answer 1

In Δ ABC, it is given that DE || BC.
Applying Thales’ theorem, we have :

`(AD)/(DB) = (AE)/(EC)`

⟹ `X/(X-2) = (X+2)/(X-1)`

⟹ `X (X-1) = (X-2) (X +2)`

⟹`X^2 - X = X^2 - 4`

⟹ X = 4 CM