In ∆ABC, P and Q are the middle points of the sides AB and AC, respectively. R is a point on the segment PQ such that PR: RQ = 1:5. If PR= 6 cm, then BC = ____.

Correct option is D

Given:
PR: RQ = 1:5
PR = 6 cm
Concept used:
The line joining the midpoints of two sides of a triangle is parallel and half of the third side
Solution :  

The ratio of PR and RQ be x and 5x respectively.
Now, according to the question
=> PR = x = 6 cm [Given]
RQ = 5x = 5x 6 = 30 cm
Now,
PQ = (PR + RQ)
PQ=(6+30) cm
PQ = 36 cm
Now,
As, The line joining the midpoints of two sides of a triangle is parallel and half of the third side
So, BC = 2PQ
BC = 2 x 36 cm
BC = 72 cm
∴ The required value of BC is 72 cm