Altitude of the hypotenuse

Question

The altitude to the hypotenuse of a right triangle divides the hypotenuse into segments 9in. long and 12 in. long. Find the length of the altitude to the hypotenuse.

Answer 1

The altitude on the hypotenuse is the mean proportional between the two segments of the hypotenuse.

 

9 / x = x / 12

x² = 108

x = 6√3