Question

Please answer.........Q.3

Answer 1

In figure PS is the median
Triangle PTS is a right angled triangle.
Therefore according to figure angle PTS is a right angle.
Therefore both the anlge that is angle TPS and angle TSP are not right angles but both of them are acute angles.
Therefore if angle TSP is acute then angle PSR has to be an obtuse angle.
Consider triangle PTR
angle PSR is an obtuse angle which I already proved.
There is a theorem which states relation between side opposite to obtuse angle with two remaining sides.
According to that theorem
PR^2 = SR^2 + PS^2 + 2SR*ST
It can be rewritten as
PR^2 = PS^2 + QR*ST + (QR/2)^2
SR^2 is rewritten as (QR/2)^2 and 2SR is rewritten as QR
Hence, proved.
Hope it helps.