the length of hypotenuse

**rcs** · December 22nd 2012, 06:25 AM

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

**skeeter** · December 22nd 2012, 06:39 AM

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

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

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

solve for $c$

**rcs** · December 22nd 2012, 07:23 AM

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?

**Soroban** · December 22nd 2012, 06:43 PM

Hello, rcs!

You are right! . . . Good work!

Thread: the length of hypotenuse