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.

Answer 1

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

AC = 21 cm, BC = 29 cm and $AB={30}^{\circ }$

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

$\therefore$ PQ || AB and $PQ=\frac{1}{2}AB$

$=\frac{1}{2}\times {30}^{\circ }=15cm$

Similarly, QR || BC and

$QR=\frac{1}{2}\times BC=\frac{1}{2}\times 29=14.5cm$

and RP || AC and $RP=\frac{1}{2}AC$

$=\frac{1}{2}\times 21=10.5cm$

Now perimeter of quad. ARPQ,

= AR+RP+PQ+AQ

$=\frac{1}{2}AB+\frac{1}{2}AC+\frac{1}{2}AB+\frac{1}{2}AC$

= AB+AC = 30+21= 51 cm