Find the length of the altitude to the hypotenuse of a right triangle whose sides have lengths 6,8,10.

Question

Find the length of the altitude to the hypotenuse of a right triangle whose sides have lengths 6,8,10.

Answer 1

First, use the theorem that says, "The length of each leg of a right triangle is the geometric mean of the lengths of the hypotenuse and the segment of the hypotenuse that is adjacent to the leg."

Let x = the length of one part of the hypotenuse

Let 10 - x = the length of the other part of the hypotenuse

Let y = the length of the altitude

10/6 = 6/x

10x = 36

x = 3.6 

10-x = 6.4

Now use the theorem that says, "In a right triangle, the altitude to the hypotenuse divides the hypotenuse into two segments. The length of the altitude is the geometric mean of the lengths of the two segments."

3.6/y = y/6.4

y² = 23.04

y = 4.8

 

Of course, you can also use similarity as Mark suggested.