SOLUTION: the altitude to the hypotenuse of a right triangle divides the hypotenuse into two segments that are x cm and 4x cm, respectively. What is the length of the altitude?

Algebra ->  Triangles -> SOLUTION: the altitude to the hypotenuse of a right triangle divides the hypotenuse into two segments that are x cm and 4x cm, respectively. What is the length of the altitude?      Log On


   

Question 844709: the altitude to the hypotenuse of a right triangle divides the hypotenuse into two segments that are x cm and 4x cm, respectively. What is the length of the altitude?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The altitude divides the right triangle into two similar right triangles.

The ratio of longer leg to shorter leg in those two triangles is the same.
If h= length of the altitude to the hypotenuse, those ratios are
h%2Fx for the smaller triangle, and
4x%2Fh for the larger one.
Since they are the same
h%2Fx=4x%2Fh
Solving for h ,
h%2Fx=4x%2Fh
h%5E2=4x%2Ax
h%5E2=4x%5E2
highlight%28h=2x%29