Question

When an altitude is drawn to the hypotenuse of a right triangle, the lengths of the segments of the hypotenuse are 4 and 9. What is the length of the altitude?

9

13

4

6

Answer 1

So, all we have to do is to find x for this question.
All you need is Pyth. Thm. here (Of course with some additions.)

In triangle ABC,
a^2 + b^2 = (4+9)^2
a^2 + b^2 = 13^2 ---(1)

In triangle ACD,
x^2 + 4^2 = b^2 ---(2)

In triangle BCD,
x^2 + 9^2 = a^2 ---(3)

(2) + (3),
(x^2 + 4^2) + (x^2 + 9^2) = a^2 + b^2
So, you can sub (1) to the right side to solve x.