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 $${\left( {\frac{{{\text{PQ}}}}{{{\text{QR}}}}} \right)^2}?$$

A. $$\frac{3}{2}$$

B. $$\frac{5}{2}$$

C. $$2$$

D. None of these

Answer: Option B

Solution (By Examveda Team)

$$\eqalign{ & PQ = PR \cr & QR = \sqrt {\frac{{P{Q^2} + P{R^2}}}{5}} \,\,\left( {{\text{By Theorem}}} \right) \cr & Q{R^2} = \frac{{2P{Q^2}}}{5} \cr & \frac{{P{Q^2}}}{{Q{R^2}}} = \frac{5}{2} \cr} $$