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 = 30 cm, find the perimeter of the quadrilateral ARPQ.

Answer 1

It is given that P, Q and R are the mid-points of BC, CA and AB respectively.

Also, we have , and

We need to find the perimeter of quadrilateral ARPQ

In , P and R are the mid-points of CB and AB respectively.

Theorem states, the line segment joining the mid-points of any two sides of a traingle is parallel to the third side and equal to half of it.

Therefore, we get:

Similarly, we get

We have Q and R as the mid points of AC and AB respectively.

Therefore,

And

Perimeter of

Hence, the perimeter of quadrilateral ARPQ is.