Question

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

• A. $2\sqrt{2}6$
• B. $2\sqrt{3}1$
• C. $\sqrt{3}1$
• D. $\sqrt{2}6$

Answer 1

The correct option is B $2\sqrt{3}1$

In $△ABC$,

Let $BM=x$

$A{B}^2+A{C}^2=2(A{M}^2+B{M}^2)$ [By Theorem]

$4^2+8^2=2(3^2+x^2)$

$16+64=2(9+x^2)\Rightarrow 80=18+2x^2$

$\Rightarrow 62=2x^2$

$\Rightarrow 31=x^2$

$\Rightarrow x=\sqrt{31}$

$BM=x$

$BC=2\times x$

$=2\sqrt{31}$