# A rectangle that is x feet wide is inscribed in a circle of radius 10 feet. How do you find the expression for the area of the rectangle as a function of x?

Oct 31, 2016

#### Explanation:

The diagonal of the rectangle is the diameter of the circle (which is twice the radius).

Using the Pythagorean Theorem :

${20}^{2} = {x}^{2} + {x}^{2}$

$400 = 2 {x}^{2}$

${x}^{2} = 200$

$x = 10 \sqrt{2}$