Question

D and E are points on the sides AB and AC respectively of a ΔABC such that DE║BC.

If `(AD)/(DB) = 4/7` and AC = 6.6cm, find AE.

Answer 1

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

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

⟹ `4/7 =(AE)/(EC)`

Adding 1 to both the sides, we get :

`11/7 = (AC)/(EC)`

⟹ EC = `(6.6 ×7)/11 = 4.2 cm`

Therefore

AE = AC – EC = 6.6 – 4.2 = 2.4 cm