# Thread: the length of hypotenuse

1. ## the length of hypotenuse

In a right triangle, the medians to the legs are sqrt 15 and sqrt 20 long. How long is the hypotenuse?

2. ## Re: the length of hypotenuse

$a^2 + b^2 = c^2$

$\left(\frac{a}{2}\right)^2 + b^2 = 20$

$\left(\frac{b}{2}\right)^2 + a^2 = 15$

solve for $c$

3. ## Re: the length of hypotenuse

Originally Posted by skeeter
$a^2 + b^2 = c^2$

$\left(\frac{a}{2}\right)^2 + b^2 = 20$

$\left(\frac{b}{2}\right)^2 + a^2 = 15$

solve for $c$

2 sqrt 7

is this correct sir?

4. ## Re: the length of hypotenuse

Hello, rcs!

You are right! . . . Good work!