All PSAT Math Resources
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 .
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 .