PQR is a triangle such that PQ = PR. RS and QT are the median to the sides PQ and PR respectively. If the medians RS and QT intersect at right angle, then what is the value of ( PQ QR )^2?

Answer: Option B

Solution

Answer: Option B

Solution:

$$\begin{array}{rl}& PQ=PR\\ & QR=\sqrt{\frac{P{Q}^2+P{R}^2}{5}}\left(\text{By Theorem}\right)\\ & Q{R}^2=\frac{2P{Q}^2}{5}\\ & \frac{P{Q}^2}{Q{R}^2}=\frac{5}{2}\end{array}$$