Question

In $△ABC,{AB}^2+{BC}^2=122,BC=10$. Find the length of the median on side $BC$.

Answer 1

Given, ${AB}^2+{BC}^2=122,BC=10$
$BP=PC=5$ cm
Let $AP$ be the median on side $BC$ of $△ABC$.
$\therefore$ ${AB}^2+{BC}^2=2{AP}^2+2{BP}^2$
(By Apollonius theorem)
$\Rightarrow 122=2{AP}^2+2{\left(5\right)}^2$
$\Rightarrow 122=2{AP}^2+50$
$\Rightarrow 122-50=2{AP}^2$
$\Rightarrow 2{AP}^2=72$
$\Rightarrow {AP}^2=36$
$\Rightarrow AP=6$
Thus, the length of the median on side $BC$ is $6$ units.