In ΔPQR, ∠P = 90°. S and T are the mid points of sides PR and PQ, respectively. What is the value of $$\frac{{{\text{R}}{{\text{Q}}^2}}}{{{\text{Q}}{{\text{S}}^2} + {\text{R}}{{\text{T}}^2}}} = ?$$

Solution (By Examveda Team)

$$\eqalign{ & {\text{RT }}\& {\text{ QS are medians}} \cr & 5{\text{Q}}{{\text{R}}^2} = 4\left( {{\text{Q}}{{\text{S}}^2} + {\text{R}}{{\text{T}}^2}} \right) \cr & \Rightarrow \frac{4}{5} = \frac{{{\text{Q}}{{\text{R}}^2}}}{{{\text{Q}}{{\text{S}}^2} + {\text{R}}{{\text{T}}^2}}} \cr} $$