Question

in a triangle ,P,Q,R are mid points of sides BC CA AB . if ac=16cm bc=20cm ab=24cm .then find perimeter of quadrilateral ARPQ

Answer 1

QP =1/2AB
=12cm

RP=1/2AC
=8cm
perimeter of quadrilateral ARPQ=8+8+12+12
=40cm

Answer 2

I'm triangle ABC,
P & Q are the mid points of BC & CA.
So, according to the mid point theorem,
PQ = 1/2 AB
PQ is parallel to BA.
So, PQ is parallel to AR............1
PQ = 1/2 AB = 1/2 * 24 = 12cm
Similarly, P & R are the mid points of BC & AB.
So, according to the mid point theorem,
PR = 1/2 AC
PR is parallel to AC.
So, PR is parallel to AQ..............2
PR = 1/2 AC = 1/2 * 16 = 8cm
Now,
As in quadrilateral ARPQ, opposite side are parellel from 1 and 2, so ARPQ is a parallelogram.
The perimeter = 2(l + b) = 2(12+8) = 2*20 = 40 cm.


The perimeter is 40 cm.