In a Δ ABC , P and Q are points on sides AB and AC respectively, su – InterviewSolution

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1.

In a Δ ABC , P and Q are points on sides AB and AC respectively, such that PQ II BC. If AP = 2.4 cm, AQ = 2 cm, QC = 3 cm and BC = 6 cm, find AB and PQ..

Answer»

WE have,

PQ∥BC

We have AP/PB = AQ/QC

2.4/PB = 2/3

PB = 3x2.4/2

PB = 3x1.2

PB = 3.6 cm

Now AB = AP+PB

AB = 2.4+3.6

AB = 6 cm

Now IN ⊿ APQ and ⊿ ABC

∠A = ∠A [Common]

∠APQ = ∠ABC [PQ∥BC]

⊿ APQ ~ ⊿ ABC [By AA criteria]

AB/AP = BC/PQ

PQ = 6x2.4/6

PQ = 2.4 cm

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