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 = 4 cm, DB = (x – 4) cm, AE = 8 cm and EC = (3x – 19) cm.  

Answer 1

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

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

⟹ `4/(x-4) = 8 /(3x -19)`

⟹ 4 (3x-19) = 8 (x-4)

⟹ 12x – 76 = 8x – 32

⟹ 4x = 44

⟹ x = 11 cm