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Question

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

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Solution

If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.

Hence AQQC=APPB

23=2.4PB

PB=3.6cm

AB=AP+PB=2.4+3.6=6cm

As PQBC

AQP=ACB

APQ=ABC

So by AAA AQPACB

Hence AQAC=QPCB

25=QP6

QP=2.4cm

So AB=6cm and QP=2.4cm

891142_969142_ans_3b79aa1b21ac425eb04b74e484bcb400.png

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