Find the Length of the Hypotenuse

Date: 05/08/2003 at 22:15:44
From: Anna
Subject: Geometry/Algebra

The medians to the legs of a right triangle are 10 and 12.649 or 
4 radical 10. Find the length of the hypotenuse.

I know that if you have the two medians, that forms two 30, 60,
90-degree triangles.  So for one they told us that the median is 10
and that's the hypotenuse of the triagle. So one leg is 5 and the
other 5 radical 3.  Then the other triangle is 4 radical 10 hypotenuse
and 2 radical 10, and then I don't know what to do from there.

Date: 05/09/2003 at 11:13:29
From: Doctor Luis
Subject: Re: Geometry/Algebra

Hi Anna,

Suppose your right triangle has sides x, y and hypotenuse c. Let the
lengths of the two medians be a = 4*sqrt(10), b = 10. You can use the
knowledge you have about medians (they bisect the opposite side) to 
find the values of x and y, and then finally, use your values of x and 
y to find the hypotenuse c. 

But why get all tangled up in words when I can show you with a nice 
diagram?

 

Now it should be pretty easy.

I hope this helped. Let us know if you have any more questions.

- Doctor Luis, The Math Forum
  http://mathforum.org/dr.math/