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. 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. x² − 120x = 1,800
d. 2x² − 120x = 1,800

Answer 1

To find the dimensions of the horse paddock, we set up an equation based on the perimeter and solve for the width. Then, using the given area, we can find the length. The dimensions are 90 feet by 20 feet.

Step-by-step explanation:

To determine the equation that can be used to find the dimensions of the horse paddock, we need to consider the perimeter of the paddock. Since one side of the paddock is the side of the barn, we only need to find the perimeter of the other three sides. Let's denote the width of the paddock as x. The perimeter of the paddock is then given by the equation 80 + x + x = 120, since the first side is 80 and the other two sides are both x. Simplifying this equation gives us 2x = 40, so the width of the paddock is x = 20 feet. Since the area of a rectangle is given by the equation Area = length × width, we can find the length of the paddock by dividing the given area of 1800 square feet by the width of 20 feet, giving us a length of 90 feet. Therefore, the dimensions of the horse paddock when the area is 1800 square feet are 90 feet by 20 feet.