Question

In $∆$PQR, $\angle$Q = 90^° , PQ = 12, QR = 5 and QS is a median. Find l(QS).

Answer 1

In △PQR,
PR² = PQ² + QR² (By Pythagoras theorem)
⇒ PR² = 12² + 5²
⇒ PR² = 144 + 25
⇒ PR² = 13²
⇒ PR = 13
In a right angled triangle, the length of the median on its hypotenuse is half the length of the hypotenuse.
$$\begin{gathered} \therefore l\left(\mathrm{QS}\right)=\frac{1}{2}\left(\mathrm{PR}\right) \\ =\frac{1}{2}\left(13\right) \end{gathered}$$
= 6.5 units.
Hence, the length of QR is 6.5 units.