Question

D and E are points on the sides AB and AC respectively of a ΔABC such that DE || BC. If `(AD)/(AB) = 8/15` and EC = 3.5 cm, find AE.

Answer 1

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

`(AD)/(AB) = (AE)/(AC)`

⟹ `8/15 = (AE)/(AE + EC)`

⟹ `8/15 = (AE)/(AE + 3.5)`

⟹ 8AE + 28 = 15AE

⟹ 7AE = 28

⟹ AE = 4cm