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

Question

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

Philoid · Accepted Answer

Given: AD/AB = 8/15 or AD = 8 cm, AB = 15 cm, and EC = 3.5 cm

By applying Thale’s Theorem,

⇒

⇒ 8×(AE + 3.5) = 15×AE

⇒ 8×AE + 28 = 15×AE

⇒ 15×AE – 8×AE = 28

⇒ 7×AE = 28

⇒ AE = 28/7 = 4

Hence, AE is 4 cm.