Question

In $△PQR$, point $S$ is the mid-point of side $QR$.If $PQ=11,PR=17$ Find $QR$

Answer 1

In $△PQR$point $S$ is the midpoint of side $QR$

$QS=SR=\frac{1}{2}QR$

${PQ}^2+{PR}^2=2{PS}^2+2{QS}^2$(by Appollonius theorem)

$\Rightarrow {11}^2+{17}^2=2{\left(13\right)}^2+2{QS}^2$

$\Rightarrow 121+289=2\left(169\right)+2{QS}^2$

$\Rightarrow 2{QS}^2=410-338=72$

$\Rightarrow {QS}^2=\frac{72}{2}=36$

$\Rightarrow QS=6$

$\therefore QR=2\times QS=2\times 6=12$

Hence, $QR=12$units.