Question

In $△ABC$, seg AQ is the median on BC. $A{B}^2+A{C}^2=122$, BC=$10$ units. Find the length of the median on side BC.

Answer 1

In $△ABC$,

AQ is the median.

$\therefore$ by Apollonius theorem,

$A{B}^2+A{C}^2=2A{Q}^2+2Q{C}^2$

$122=2A{Q}^2+2{\left(\frac{1}{2}BC\right)}^2$

$122=2A{Q}^2+2{(\frac{1}{2}\times 10)}^2$

$122=2A{Q}^2+2(5{)}^2$

$122-50=2A{Q}^2$

$2A{Q}^2=72$

$A{Q}^2=36$

$\therefore AQ=6$