area of a rectangle inscribed in a circle

[zzinfinity]

I'm having trouble with the following problem.
What are the dimensions of the rectangle of the greatest area which can be inscribed in a circle of radius 2?

I'm not sure how to get an equation for the area of the rectangle. Once I have an equation I know how the find the maximum, I just need help finding the area equation.

Thanks!

 

[galactus]

Center the circle at the origin and draw a rectangle in the center. The length of the rectangle is 2x and the height is 2y.

The area of the rectangle is then \(\displaystyle A=4xy\)

Draw a line from the origin to a point of the circle forming the radius.

\(\displaystyle x^{2}+y^{2}=4\)

\(\displaystyle y=\sqrt{4-x^{2}}\)

\(\displaystyle A=4x\sqrt{4-x^{2}}\)

Differentiate, set to 0 and solve for x.

Sub this value back into y and A to find y and the area.