The altitude of a right triangle from the vertex of its right triangle to its hypotenuse divides it into two similar triangles.

, as the length of the altitude corresponding to the hypotenuse, is the geometric mean of the lengths of the parts of the hypotenuse it forms; that is, it is the square root of the product of the two:

.

The ratio of the smaller sides of these similar triangles is

The ratio of the smaller side of to that of is

or : 1,

so this is also the ratio of the perimeter of to that of .