To find the area of the rectangle, we first need to establish the relationship between the length and width based on the information given.
Let’s denote the width of the rectangle as w. Since the length is twice the width, we can express the length as l = 2w.
The formula for the perimeter P of a rectangle is given by:
P = 2(l + w)
Substituting the values we have:
60 = 2(2w + w)
60 = 2(3w)
60 = 6w
Now, to find the width, we can divide each side of the equation by 6:
w = 60 / 6 = 10 ft
Now that we know the width, we can find the length:
l = 2w = 2(10) = 20 ft
With both dimensions known, we can calculate the area A of the rectangle using the formula:
A = l × w
Substituting the known values:
A = 20 × 10 = 200 ft²
Therefore, the area of the rectangle is 200 square feet.