In ΔABC, D and E are points on AB and AC respectively such that AD = 5 cm, DB = 8 cm and DE || BC. If AC = 6.5 cm, then find AE.

Question

Philoid · Accepted Answer

Given :

AD = 5 cm

DB = 8 cm

AC = 6.5 cm

DE ||BC

In ΔABC & ΔADE

∠ADE = ∠ABC (Corresponding Angles)

∠AED = ∠ACB (Corresponding Angles)

So ΔABC & ΔADE are similar by the A.A. (Angle-Angle) axiom of Similarity

AB = AD + BD = 13 cm.

Since the two triangles are similar so their lengths of sides must be in proportion.

⇒

AE = 2.5cm.