Question

Refer to this figure to complete this proportion answers are A) c B) r C) s D) H

Answer 1

The altitude from the right angle of a right triangle makes two triangles that are similar to the original. That's proven by AA because they all have right angles and each shares an angle with the larger triangle.

r/h is the ratio of the short leg r to the long leg h of the smallest of these triangles.

For ?/s to be equal it must the ratio of the short leg ? to the long leg s. So ? is the short leg of the medium sized triangle, h.

$\dfrac r h = \dfrac h s$

$h^2 = rs$

The altitude is the geometric mean of the partitioned segments of the hypotenuse.

Answer: Last choice h