(99 points) using similarity solve for x. show all work

General Idea:

In any right triangle,

1. The altitude to the hypotenuse is the geometric mean between the segments into which is separates the hypotenuse.

2. Each leg is a geometric mean of the hypotenuse and the segment of the hypotenuse adjacent of the leg.

Applying the concept:

Step 1: We need to label the given diagram and set up a proportion by comparing the similar triangles as provided in attached figure.

Setting up the proportion, we get...

Conclusion:

Shorter Length/Hypotenuse = ab/ac = ad/ab

x/9+16 = 9/x

x^2 = 9 x (9 + 16)

= 9 x 25

= 225

square root of 225 = 15

x = 15

lol

step-by-step explanation: