Question

P,Q,R are the midpoints of sides of triangle ABC respectively.Find the ratio of perimeters of triangle PQR and triangle ABC.

Answer 1

Given, 
P , Q, R are midpoints of AB, BC and CA respectively.

Please refer attached image:

Hence, 
[tex] \frac{Perimeter of triangle ABC}{Perimeter of triangle PQR} = \frac{2}{1} = 2:1 [/tex]

Answer 2

Solution :-

P, Q and R are the midpoints of sides AB, BC and AC of triangle ABC.

By mid point theorem,

⇒ PR = 1/2 of BC = PR/BC = 1/2......(1)

⇒ PQ = 1/2 of AC = PQ/AC = 1/2 .....(2)

⇒ QR = 1/2 of AB = QR/AB = 1/2 ......(3)

Hence, Perimeter of Δ ABC/Perimeter of Δ PQR

= (AB + BC + CA)/(PQ + QR + RP)

= (AB + BC + AC)/1/2(AB + BC + AC)

= 1/2

Answer.