Question 844962
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.