# How do you maximize the perimeter of a rectangle inside a circle with equation: #x^2+y^2=1#?

##### 1 Answer

#### Explanation:

For symmetry reasons we can assume the rectangle has sides parallel to the axes. In such case if the corner in the first quadrant is the point

so that:

and the perimeter is:

Evaluate the first derivative:

And identify critical points solving the equation:

Evaluate the second derivative:

so that the critical point is a local maximum.

Then the perimeter is maximum when