The length of a rectangle is six times its width. If the perimeter of the rectangle is 140ft, find its area.
P = 2L + 2W
140 = 2(6W) + 2W
140 = 14W
10 = W
L = 6W
L = ?
A = LW
A = ?
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To find the area of a rectangle, we need to know the length and width.
Let's say the width of the rectangle is represented by w, in feet.
According to the given information, the length of the rectangle is six times its width, so the length can be expressed as 6w.
The perimeter of a rectangle is given by the formula:
Perimeter = 2 * (Length + Width).
In this case, the perimeter is given as 140 ft, so we can substitute the values into the formula and solve for w:
140 = 2 * (6w + w)
Simplifying the equation:
140 = 2(7w)
70 = 7w
w = 10
Now that we know the value of w, we can find the length of the rectangle:
Length = 6w
Length = 6*10
Length = 60
The width of the rectangle is 10 ft, and the length is 60 ft.
To find the area of the rectangle, we use the formula:
Area = Length * Width
Area = 60 * 10
Area = 600 square feet.
Therefore, the area of the rectangle is 600 square feet.