Question

P, Q and R are the midpoints of the sides BC, CA and AB of Δ ABC. Prove that: Perimeter of triangle QPR
= ½ (Perimeter of triangle ABC).

Answer 1

Answer:

If R, Q and P are the midpoints of AB, AC and BC, and by applying the theorem:-

The line segment joining the midpoints of two side of a triangle is parallel to the third side and equal to half of it, we get

PQ=

2

1

AB=AR and PQ∣∣AR

PQ=

2

1

AC=AQ and PR∣∣AQ

Since the above conditions are sufficient for a parallelogram, therefore ARPQ is a parallelogram.

∴ Perimeter of ∥

gm

=ARPQ=2(AR+AQ)=AB+AC=(30+21)cm=51cm

solution