Question

Two rectangular corral’s are to be made from 120 yds of fencing as seen below. If the rancher wants the total area to be 600 yd 2 , what dimensions should be used to make each of the corral’s?

Answer 1

The answer is below

Explanation:

The perimeter of the rectangle is given as:

Perimeter = x + x + y + y + y = 2x + 3y

2x + 3y = 120

2x = 120 - 3y

Dividing through by 2:

x = 60 - 3y/2

The area of the rectangle is given by:

Area (A) = x * y

A = (60 - 3y/2)(y)

A = 60y - 3y² / 2

But the total area = 600 yd², hence

600 = 60y - 3y²/2

multiply through by 2:

1200 = 120y - 3y²

3y² - 120y + 1200 = 0

3y² - 60y - 60y + 1200 = 0

3y(y - 20) - 60(y - 20) = 0

(3y - 60)(y - 20) = 0

3y - 60 = 0, or y - 20 = 0

3y = 60 or y - 20 = 0

y= 20

x = 60 - 3y/2

x = 60 - 3(20)/2

x = 60 - 30

x = 30