Mr. Pilgram needs fencing for his turkey coop. The perimeter is 240 yards. The length is 16 yards longer than the width. What are the dimensions? What is the area?
P = 2L + 2W
240 = 2(W + 16) + 2W
240 = 4W + 32
208 = 4W
52 = W
To find the dimensions and area of the turkey coop, we can set up equations based on the given information.
Let's assume the width of the turkey coop is "x" yards. Since the length is given as 16 yards longer than the width, the length will be "x + 16" yards.
The perimeter of the turkey coop is the sum of all the sides, which is 240 yards. Considering that a rectangle has two equal lengths and two equal widths, we can set up the following equation:
Perimeter = 2 * (length + width)
Substituting the given values:
240 = 2 * (x + 16 + x)
Now, let's solve this equation to find the value of "x."
First, distribute the 2:
240 = 2x + 32 + 2x
Combine like terms:
240 = 4x + 32
Subtract 32 from both sides:
240 - 32 = 4x
208 = 4x
Divide both sides by 4:
208/4 = x
x = 52
Therefore, the width of the turkey coop is 52 yards.
Since the length is given as "x + 16," we can substitute the value of x to find the length:
Length = 52 + 16 = 68 yards.
The dimensions of the turkey coop are 52 yards (width) and 68 yards (length).
To find the area of the turkey coop, we use the formula:
Area = Length * Width
Substituting the values:
Area = 52 * 68
Calculating:
Area = 3,536 square yards.
Therefore, the area of the turkey coop is 3,536 square yards.