Question

In ∆ABC, DE ║ BC such that AD/DB = 3/5 . If AC = 5.6cm, then AE = ? 

(a) 4.2cm 

(b) 3.1cm 

(c) 2.8cm 

(d) 2.1cm

Answer 1

(d) 2.1 cm 

It is given that DE || BC. 

Applying Thales’ theorem, we get: 

AD/DB = AE/EC 

Let AE be x cm. 

Therefore, EC = (5.6 – x) cm 

⇒ 3/5 = x/5.6 − x

⇒ 3(5.6 − x) = 5x

⇒ 16.8 − 3x = 5x

⇒ 8x = 16.8 

⇒ x = 2.1 cm