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) -2x²+120x= 1800
b) -x²+120x= 1800
c) x²+120x= 1800
d) 2x²+120x= 1800

Answer 1

The correct equation to find the dimensions of the horse paddock with an area of 1,800 square feet, using the side of the barn as one side and letting x represent the width, is -2x² + 120x = 1800, which is option (a).

Step-by-step explanation:

To determine which equation can be used to find the dimensions of the horse paddock with an area of 1,800 square feet, where Jill is using the side of the barn as one side of her paddock, we need to set up an equation that accounts for the perimeter and area of the paddock. Since the fencing will only be covering three sides (2 widths and 1 length), if we let x represent the width, then the remaining length would be 120 - 2x feet because Jill has 120 feet of fencing in total.

The area of the paddock can be found by multiplying the width by the length. Therefore, the area A can be expressed as:

A = x * (120 - 2x)

This simplifies to:

A = 120x - 2x²

Since we know the area is supposed to be 1,800 square feet:

1800 = 120x - 2x²

And if we rearrange the terms to match the given equations, we get:

-2x² + 120x = 1800

Therefore, the correct equation to find the dimensions of the horse paddock when the area is 1,800 square feet, letting x represent the width, is:

-2x² + 120x = 1800

Which corresponds to option (a).

Answer 2

The correct equation 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, is option a) -2x² + 120x = 1800.

Step-by-step explanation:

Jill has 120 feet of fencing to use for her horse paddock and wants to use the side of the barn as one side of the rectangle. She needs to determine which equation can be used to find the dimensions of the paddock when the area is 1,800 square feet. Letting x represent the width of the paddock, the total fencing used for the other three sides would be 2x (2 widths) plus the length of the side along the barn. Since the length of the side along the barn does not require fencing, it would be (120 - 2x). The area of the rectangle is length times width, so:

x(120 - 2x) = 1800

Expanding this equation:

120x - 2x² = 1800

Since we want the area to be 1800 square feet, we rearrange the equation to:

-2x² + 120x = 1800

Thus, the correct equation to represent this scenario is option a) -2x² + 120x = 1800.