[ Mean proportional in a right triangle ]

The height of a right triangle, drawn from the vertex of the right angle, divides the hypotenuse into segments equal to $a$ and $b$. Find the legs.

#
Each leg of a right triangle is the mean proportional between the hypotenuse and its projection on the hypotenuse.

## Answer

$$
\sqrt{a(a+b)}, \sqrt{b(a+b)}
$$