# How do you find the maximum area of rectangle with 80ft perimeter?

##### 1 Answer

Algebraically, we can show that the maximum area of the rectangle is achieved when it is a square. In this case, the maximum area is

#### Explanation:

Since this is not in calculus, I'll provide a non-calculus answer.

We know the rectangle always has a perimeter of

We also know that the area of the rectangle is

Use the perimeter expression

#A=lw#

#A=(40-w)w#

#A=-w^2+40w#

This quadratic function can be graphed, and the highest point will be the spot where the rectangle's area is maximized.

graph{-x^2+40x [-5, 45, -145, 460]}

The highest point, the vertex of the parabola, is