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

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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»

(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

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