Question 243047: The perimeter of a rectangle is 16 times the width. THe length us 12cm more than the width. WHat is the length and width of the rectangle? I can't figure out the formula to solve the problem.
Answer by oberobic(2304)   (Show Source):
You can put this solution on YOUR website! We know the perimeter of a rectangle = P = 2W + 2L, where W=width and L=length.
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We are told P = 16W, so 16W = 2W + 2L.
Subtracting 2W from both sides:
14W = 2L
Dividing by 2:
7W = L
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We are told L-12=W.
Substituting for L, we have
7W-12 = W
Adding 12 to both sides
7W = W + 12
Subtracting W from both sides
6W = 12
Dividing by 6
W = 2
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Since L is 12 more than W (given), we have
L = W + 12 = 2 + 12 = 14
L = 14
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To check our work, let's substitute back into the givens.
P = 2(2) + 2(14) = 4 + 28 = 32.
Is 32 = 16W? Yes it is.
Done.
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