A farmer decides to build a fence to enclose a rectangular field in which he will plant a crop. He has 1300 1300 feet of fence to use and his goal is to maximize the area of his field. What is the width of the field if the length of the field is 250 250 feet?

The width of the field is 400 ft.

Explanation:

Hi there!

let x be the width of the field. The perimeter is 1300 ft and is the sum of each side of the rectangle. Then:

perimeter = 2 · length + 2 · width

1300 ft = 2 · 250 ft + 2 · x

Let's solve this equation for x

1300 ft = 500 ft + 2x

Substract 500 ft to both sides of the equation.

1300 ft - 500 ft = 2x

800 ft = 2x

Divide by 2 both sides of the equation.

800 ft/2 = x

x = 400 ft

The width of the field is 400 ft.