Question

In triangle ABC, DE// BC , AD = 3 cm,DB = 4 cm,DE = 2 cm and BC = x cm then x equals to

Answer 1

Given : In triangle ABC, DE// BC , AD = 3 cm,DB = 4 cm,DE = 2 cm and BC = x

To Find :  Value of  x

Solution:

Comparing ΔADE & ΔABC

∠A =∠A  ( common Angles)

∠ADE = ∠ABC    ( corresponding angles DE║BC )

∠AED  = ∠ACB   ( corresponding angles DE║BC )

ΔADE ≈ ΔABC   (AAA )

=> AD/AB = DE/BC

AD = 3

DB = 4

AB = AD + DB = 3 + 4 = 7

DE = 2

BC = x

=> 3/7 = 2/x

=> x = 14/3

x = 14/3

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