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

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

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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