Question

Jill has 120 feet of fencing to use for her horse paddock. To increase the area she can enclose, she plans on using the side of the barn as one side of her paddock as shown below.

A rectangle-shaded area is labeled paddock. A broken line from the left to the right on the top of the rectangle area is labeled Barn.

Determine which equation can be used to find the dimensions of the horse paddock when the area is 1,800 square feet. Let x represent the width of the paddock.

A.
x2 − 120x = 1,800
B.
2x2 − 120x = 1,800
C.
-2x2 + 120x = 1,800
D.
-x2 + 120x = 1,800

Answer 1

Use three sides of fencing: two widths x plus one length L gives 2x + L = 120, so L = 120 − 2x. Area = x·L = x(120 − 2x) = 120x − 2x^2. Setting this equal to 1800 gives −2x^2 + 120x = 1800.

Answer: C.