In the figure we have three right angles .The triangles similar to each other .Similar triangles have sides in proportion .The altitude rule is true for the triangles .
The theorem states :The altitude to the hypotenuse of a right triangle is the mean proportional between the segments into which it divides the hypotenuse.
[tex] \frac{part of hypotenuse}{altitude} =\frac{altitude}{other part hypotenuse } [/tex]
Substituting the values from the triangles we ahve:
[tex] \frac{r}{h} =\frac{h}{s} [/tex]
s is the right answer
