SOLUTION: The sides of a rectangle are in the ratio of 3:2. What is the length of each side if the perimeter of the rectangle is 55 cm?
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Question 499755: The sides of a rectangle are in the ratio of 3:2. What is the length of each side if the perimeter of the rectangle is 55 cm?
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
Perimeter = 2*Length + 2*Width = 2L+2W = 2(L+W)
P = 55 cm
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The tricky part here is to model the ratio of L:W = 3:2
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We could try:
L/W = 3/2
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L = 3/2*W
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Substitute for L in the perimeter equation.
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2(3/2*W + W) = 55
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Multiply through
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3W + 2W = 55
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Collect
5W = 55
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Divide both sides by 5
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W = 11
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L = 3/2*W
L = 33/2
L = 16.5
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Check perimeter.
2*16.5 = 33
2*11 = 22
Total = 55
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Is the ratio 3:2?
Yes.
16.5/11 = 1.5 = 3/2
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Re-read question to see what the answer should be:
What is the length?
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The length = 16.5 cm.
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Done.
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