# A rectangular garden has a perimeter of 120 feet. How do you find an equation for the area of the rectangle as a function of the width, then determine the length and width of the rectangle which provide the maximum area?

May 19, 2018

See below

#### Explanation:

We call x to width and y to high

If perimeter is 120, then $2 x + 2 y = 120$, or $y = 60 - x$

The surface s(x)=x·y=x(60-x) is the surface area as function of width

If we want to maximize area, then s´(x)=60-2x=0 and we obtain as solution $x = 30$ and then the surface will be maximum if rectangle is a square with 30 ft of side