Finding the dimensions of a rectangle with max area that can be in a circle

Question

Find the dimensions of a rectangle with the max area that can be inscribed in a circle of radius 10.

Answer 1

Draw a figure.

Let the radius of the circle be 1.

The area of a rectangle with corners on the circle will be given by

A = 2x * 2sqrt(1-x²) = 4xsqrt(1-x²)

dA/dx= 4{[-x²/sqrt(1 - x²)] + sqrt(1 - x²)}

Set the derivative = 0 and solve for x.

You should find that the rectangle you want is a square!