Question

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?

Answer 1

See below

Explanation:

We call x to width and y to high

If perimeter is 120, then `2x+2y=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