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.

Answer 1

To find the dimensions of Jill's horse paddock with an area of 1,800 square feet using 120 feet of fencing and the barn as one side, we use the equation 120 = 2x + (1,800/x) where x is the width of the paddock.

Step-by-step explanation:

To determine which equation can be used to find the dimensions of the horse paddock when the area is 1,800 square feet and Jill has 120 feet of fencing to use, with the side of the barn representing one side of the paddock, we can follow these steps:

1. Let x represent the width of the paddock.
2. Since one side is along the barn, only three sides need fencing. Therefore, the total fencing used for the two widths and one length is 120 feet. The equation representing the perimeter is P = 2x + L, where P is the total length of the fencing (120 feet) and L is the length of the paddock.
3. To incorporate the given area of the paddock (1,800 square feet) into our calculations, we use the formula A = x * L, where A is the area.
4. Combining the above equations, we need to solve for one variable in terms of the other. Substituting for L from the perimeter equation, we have 120 = 2x + (1,800/x), which can be rearranged to find the dimensions of the paddock.