Question

In A ABC, P & Q are mid point of sides AB and AC. If BC = 8.2 cm then find PQ.

Answer 1

Answer

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

QC

AQ

=

PB

AP

3

2

=

PB

2.4

PB=3.6cm

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

As PQ∥BC

∠AQP=∠ACB

∠APQ=∠ABC

So by AAA △AQP∼△ACB

Hence

AC/AA = CB/QP

2/5=QP/6

QP=2.4cm

So AB=6cm and QP=2.4cm

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