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