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.
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.

2x2 - 120x = 1,800
-x2 + 120x = 1,800
x2 - 120x = 1,800
-2x2 + 120x = 1,800

Answer 1

Answer: -x2 + 120x = 1,800

She plans on using the side of the barn as one side of her paddock so it has 3 sides. Since the width is shorter, it will be more efficient to have 2 widths (1 lengths and 2 widths). Because Jill has 120 feet of fencing to use, you can get this equation:
120ft= 1L +2W
1L= 120-2W

If you insert it into area formula it would be:
area= L*W
area= (120-2W) *W
area= 120W- 2W^2
-2W^2+120W= area

Since x represent the width of the paddock and the area is 1800 the equation become
-2X^2+120X= 1,800