PSAT Math : How to find the height of a right triangle

Example Questions

Example Question #1 : How To Find The Height Of A Right Triangle

Note: Figure NOT drawn to scale.

Refer to the above diagram. Give the ratio of the perimeter of  to that of .

Explanation:

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 .