Question

In the given figure, ∠ABC = ${90}^{\circ }$ and BM is a median, AB = 8 cm and BC = 15 cm. Then, the value of CM is

• A. MC = 8.5 cm.
• B. MC = 6.5 cm.
• C. MC = 8 cm.
• D. MC = 7.5 cm.

Answer 1

The correct option is A

MC = 8.5 cm.

$AC=\sqrt{{AB}^2+{BC}^2}$

$AC=\sqrt{8^2+{15}^2}$

$AC=\sqrt{64+225}$

$AC=\sqrt{64+225}=\sqrt{289}=17cm.$

Since median divides the side in two parts AM = MC

So, AM = MC = $\frac{17}{2}=8.5cm$