Question

A rancher has 1600 feet of fencing to enclose a rectangular pig pen. However, one side of the pen lies along a river and requires no fencing. Express the area of the pen, A, as a function of x.

Answer 1

Answer:

$A = 2x^2-1600x$

Step-by-step explanation:

Let the dimensions of the pen be x and y.

Area, A = xy

Let y be the side oppossite the river, therefore:

The perimeter of the pen = 2x+y

Since the rancher has 1600 feet of fencing to enclose the pen.

2x+y=1600

We make y the subject of the formula

y=2x-1600

Substitute y=2x-1600 into the area function

A = x(2x-1600)

The area of the pen as a function of x is therefore:

$A = 2x^2-1600x$

Answer 2

Answer:

A(x)=x(800-x/2)

Step-by-step explanation:

Let the dimensions of the pen be x and y.

Area, A = xy

Let y be the side oppossite the river, therefore:

The perimeter of the pen = 2x+y

Since the rancher has 1600 feet of fencing to enclose the pen.

2x+y=1600

We make y the subject of the formula

y=1600-2x

Substitute y=1600-2x into the area function

A = x(1600-2x)