Question 530705
Reducing the length by 4 and the width by 2 results in an area that is 24 sq ft less than the original area.
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(L-4)*(W-2) = (L*W)-24
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We have two unknowns, so we need another equation to solve this.
Fortunately, we are told:
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L = 2W
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Substitute
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(2W-4)(W-2) = (2W*W)-24
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2W^2 -4W -4W +8 = 2W^2 - 24
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subtract 2W^2 from both sides
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-8W + 8 = -24
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subtract 8 from both sides
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-8W = -32
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divide both sides by -8
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W = 4
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L = 2W = 2*4 = 8
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L*W = 4*8 = 32
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check using the reduced dimensions to see the effect on area
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L-4 = 8-4 = 4
W-2 = 4-2 = 2
Area = 2*4 = 8
8 is 24 less than 32
correct
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Answer:  The original dimensions are 8 by 4 ft.  The reduced dimensions are 4 by 2 ft.
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Done.