# Given a perimeter of 180, how do you find the length and the width of the rectangle of maximum area?

##### 1 Answer

Sep 24, 2016

Given a perimeter of 180, the length and width of the rectangle with maximum area are 45 and 45.

#### Explanation:

Let

The area of the rectangle

Solve for

Substitute for

This equation represents a parabola that opens down. The maximum value of the area is at the vertex.

Rewriting the area equation in the form

The formula for the

The maximum area is found at

and

Given a perimeter of 180, the dimensions of the rectangle with maximum area are 45x45.