Question

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

Answer 1

In $△ABC$, applying Pythagoras Theorem,

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

$\Rightarrow A{C}^2=8^2+6^2=64+36=100$

$\Rightarrow AC=\sqrt{100}=10cm$
( 1 mark )

Therefore, $AM=MC=5cm$

Since, the mid point of the hypotenuse of a right angled triangle is equidistant from its vertices, so

$BM=AM=MC=5cm$
( 1 mark )