Question

Okay, I need some help with a couple of problems.. ^^; First, if the altitude drawn to the hypotenuse of a right triangle divides the hypotenuse into two segments with lengths of 9 inches and 17 inches, what is the exact length of the altitude?

Answer 1

Let x = length of altitude.

9 is to x as x is to 17

9/x = x/17
x^2 = ± √ (9)(17)
x = ± 3 √17
x = 3 √17

Answer 2

Theorem: The altitude drawn to the hypotenuse of a right triangle is the geometric mean between the segments of the hypotenuse. In this context, the geometric mean is a positive number.