Question

In a ABC, P. Q, R are mid points of sides BC, CA and AB respectively. If AC = 10 cm, BC = 20 cm
and AB = 20 cm, then the perimeter of ARPQ will be :
(1) 60 cm
(2) 30 cm
(3) 40 cm
(4) None of these
​

Answer 1

Answer:

Step-by-step explanation:

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.

Not sure of the answer.