The altitude drawn to the hypotenuse of a right triangle divides the hypotenuse into segments of lengths 4 and 12. Find the length of the shorter leg of the right triangle.

Answer 1

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

4 : a :: a : 12

48 = a²

4√3 = a

Now use Pythagoras to determine length of short left of the original triangle.