Question 844962: The length of a rectangle is four times its width. If the perimeter of the rectangle is 80cm, find its area.
Answer by pmesler(52)   (Show Source):
You can put this solution on YOUR website! We already know that the length is 4 times the width. We can write this as 4w. Next, we need to know the formula for the perimeter of a rectangle. The formulas is this:
P = 2l + 2w
From the information given we know that l = 4w, since it states that the length is 4 times the width.
Next, we simply SUBSTITUTE the value for l into the formula to find the perimeter and that will allow us to solve for w. We know that the perimeter is 80cm so we can just write that,
80 = 2(4w) + 2w
Now, let's solve for w.
80 = 8w + 2w
80 = 10w
Divide each side by 10
8=w. Therefore the width is 8cm and the length l = 4w or 4(8) = 32 cm.
The area of a rectangle is A = L * W. Since we know what the length and width are we simply substitute their values into the equation and we get
32 * 8 = 256 cm^2. Therefore the area of the rectangle is 256 cm^2.
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