15. The altitude of the hypotenuse of a right triangle divides the hypotenuse into segments of lengths 4 cm. and 9 cm. What is the length of the altitude?

Answer 1

altitude h
side beside 4= a
side beside 9 = b
h^2 + 16 = a^2
h^2 + 81 = b^2
-------------------- add
2h^2 + 97 = a^2 + b^2 = 13^2 = 169
2 h^2 = 72
h = 6

Answer 2

using similar triangles,
4/x = x/9
x^2 = 36
x = 6