The medians of a right angle triangle which are drawn from the vertices of the acute angles are 5 cm and 2 √10 cm. What is the length of the hypotenuse?

I am getting the answer as √13cm , but, I am still doubtful about the answer, so , I just wanted to confirm.

Consider a right angled triangle ABC having right angle at B and A and C be the acute angle.

Given, AD and CE are the median of side BC and AB.

⇒ CD = BD and AE = BE

Let AD = 5 cm and CE = 2√10 cm

In right ΔBEC, we have

In right ΔABD, we have

On putting value of BD in (1), we get

Again, in ΔABC, by Pythagoras theorem

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