Question

In a $△ABC$, $AB=4$ cm and $AC=8$ cm. If M is the midpoint of BC and $AM=3$ cm, then the length of $BC$ in cm is:

• A. $2\sqrt{26}$
• B. $2\sqrt{31}$
• C. $\sqrt{31}$
• D. $\sqrt{26}$

Answer 1

The correct option is B $2\sqrt{31}$

Given : In $△ABC$, $AB=4$ cm and $AC=8$ cm.

M is the midpoint of BC and $AM=3$ cm

Using Apollonius theorem,

$A{B}^2+A{C}^2=2(A{M}^2+B{M}^2)$

$⟹$ $4^2+8^2=2(3^2+B{M}^2)$

$⟹$ $16+64=2(9+B{M}^2)$

$⟹$ $B{M}^2=31$

$⟹$ $BM=\sqrt{31}$.

$\because$ $BC=2BM$

$\therefore$ $BC=2\sqrt{31}$.