Question

The altitude of the hypotenuse of a right triangle divides the hypotenuse into two segments. If the ratio of lengths of the segments is 1:9 and the length of the altitude is 6 meters, find the lengths of the two segments?

Answer 1

• 2 m
• 18 m

Explanation:

You want the lengths of the segments of the hypotenuse of a right triangle when an altitude of 6 m divides the hypotenuse into parts with the ratio 1:9.

Geometric mean

The altitude to the hypotenuse of a right triangle is the geometric mean of the parts it divides the hypotenuse into. If the shorter part is x, then the longer part is 9x, and their geometric mean is ...

6 = √(x(9x)) = 3√x² = 3x

x = 2 . . . . . . . divide by 3

The length of the shorter segment is 2 m; the longer one, 18 m.