SOLUTION: The expression 2(1 + w) may be used to find the perimeter of a rectagle. What are the length and width of a rectangle if the area is 13 1/2 square feet and the length of one side

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Question 20563: The expression 2(1 + w) may be used to find the perimeter of a rectagle. What are the length and width of a rectangle if the area is 13 1/2 square feet and the length of one side is 1/5 the measure of the perimeter?

Thanks,
Teri
Answer by askmemath(368) About Me  (Show Source):
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The expression 2(1 + w) may be used to find the perimeter of a rectagle. What are the length and width of a rectangle if the area is 13 1/2 square feet and the length of one side is 1/5 the measure of the perimeter?
Let length = L and width = W
We know area = LxW which is given to be 13.5 sq feet.
Also L = 1+x+Perimeter%2F5+
L = 1x+2%28L%2BW%29%2F5
Multiplying both sides with 5
5L = 2(L+W)
5L = 2L+2w
Subtracting 2L on both sides
3L = 2W
Dividing both sides with 3
L = 2W%2F3
Substituting this back in the area
Wx2W%2F3 = 13.5
Multiplying both sides with 3
2W%5E2 = 40.5
Dividing both sides with 2
W^2 = 20.25
or W = 4.5
which means L = 2/3 X 4.5 = 3