Gary's backyard is in the shape of a rectangle. his backyard is completely surrounded by 480 feet of fencing. The length of his backyard is 18 feet longer than its width. What is the area of Gary's backyard in square feet?
480=2L+2W
L-18=W
480=2(18+W) + 2W
solve for w, then L, then L x W for area
I think W is 111 and L is 129
To find the area of Gary's backyard, we need to determine its length and width. We are given that the backyard is in the shape of a rectangle, and its length is 18 feet longer than its width.
Let's assume the width of the backyard is x feet. Therefore, the length of the backyard would be x + 18 feet.
We are also given that the entire backyard is surrounded by 480 feet of fencing. This means that the sum of all sides of the rectangle is equal to 480 feet.
Since a rectangle has two pairs of equal sides, we can set up an equation:
2 * (length + width) = perimeter
Substituting the values we have:
2 * (x + (x + 18)) = 480
Simplifying:
2 * (2x + 18) = 480
4x + 36 = 480
Next, we need to solve for x:
4x = 480 - 36
4x = 444
x = 444 / 4
x = 111
So, the width of the backyard is 111 feet, and the length would be x + 18, which is 111 + 18 = 129 feet.
Now, to find the area, we multiply the length and width:
Area = length * width
Area = 129 * 111
Area = 14,319 square feet
Therefore, the area of Gary's backyard is 14,319 square feet.