Given right triangle ABC with altitude BD drawn to hypotenuse AC. If AC =16 and DC=5 what is the length of BC in the simplest radical form

The length of BC is .

Solution:

Given ABC is a right triangle.

AC is the hypotenuse and BD is the altitude.

AB and BC are legs of the triangle ABC.

AC = 16 and DC = 5

Leg rule of geometric mean theorem:

Do cross multiplication.

Taking square root on both sides.

square and square roots get canceled, we get

The length of BC is .