Question 418292: the length of a rectangle is 4 meters less than 3 times the width. If the perimeter is 56 meters, find the length and width of the rectangle.
Answer by oberobic(2304)   (Show Source):
You can put this solution on YOUR website! Start by turning the words into equations.
l = length
w = width
length = 3*width - 4
l = 3*w - 4
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P = perimeter = 2(l+w) = 2l + 2w, which is a known equation for a rectangle.
P = 56 is given
2l + 2w = 56
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Substituting what we know l equals.
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2(3w-4) + 2w = 56
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Multiply by 2 to remove the parenthesis.
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6w - 8 + 2w = 56
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Collect terms
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8w - 8 = 56
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Add 8 to both sides
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8w = 64
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Divide both sides by 8
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w = 8 = width
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Looking back, we see
l = 3w -4 = 3(8) - 4 = 24 - 4 = 20 = length
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Always check your work. In this case, if the width = 8 and the length = 20, is the perimeter 56?
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2(20)+2(8) = 40 + 16 = 56.
Yes it is.
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Remember to state the answer.
The length=20 and the width=8.
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Done.
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