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Question

In a triangle, P, Q and R are the mid-points of sides BC, CA and AB respectively. If AC = 21 cm, BC = 29 cm and AB = 30cm, find the perimeter of the quadrilateral ARPQ.

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Solution

P, Q. R are the mid -points of sides BC, CA and AB respectively

AC = 21 cm, BC = 29 cm and AB=30

P, Q, R and the mid points of sides BC, CA and AB respectively.

PQ || AB and PQ=12AB

=12×30=15cm

Similarly, QR || BC and

QR=12×BC=12×29=14.5cm

and RP || AC and RP=12AC

=12×21=10.5cm

Now perimeter of quad. ARPQ,

= AR+RP+PQ+AQ

=12AB+12AC+12AB+12AC

= AB+AC = 30+21= 51 cm


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