Question

In the given figure, $△ABC={90}^o$ and $BM$ is a median, $AB=8cm$ and $BC=6cm$. Then, length $BM$ is equal to:

• A. $3cm$
• B. $4cm$
• C. $5cm$
• D. $7cm$

Answer 1

The correct option is C $5cm$

Given: $△ABC$, $\angle B={90}^{\circ }$ and BM is median AC

By Apollonius Theorem,

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

$8^2+6^2=2(B{M}^2+5^2)$

$64+36=2(B{M}^2+25)$

$50=B{M}^2+25$

$B{M}^2=25$

$\therefore BM=5$ cm