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Question: The lengths of the medians through acute angles of a right angled triangle are 3 and 4. Its area is ...

The lengths of the medians through acute angles of a right angled triangle are 3 and 4. Its area is –

A

11\sqrt{11}

B

112\frac{\sqrt{11}}{2}

C

2311\frac{2}{3}\sqrt{11}

D

4311\frac{4}{3}\sqrt{11}

Answer

4311\frac{4}{3}\sqrt{11}

Explanation

Solution

Using Apollonous theorem sides are 43\frac{4}{\sqrt{3}} and 21132\sqrt{\frac{11}{3}}.

So area = 4311\frac{4}{3}\sqrt{11}