SOLUTION: at the touch of a button, a car shrinks by 2 feet in the width and 4 feet in the length. The original car base is 24 sq ft larger than that of the shrunken car. If the original car
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-> SOLUTION: at the touch of a button, a car shrinks by 2 feet in the width and 4 feet in the length. The original car base is 24 sq ft larger than that of the shrunken car. If the original car
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Question 530705: at the touch of a button, a car shrinks by 2 feet in the width and 4 feet in the length. The original car base is 24 sq ft larger than that of the shrunken car. If the original car's length is twice the with, find the dimensions of both cars. Answer by oberobic(2304) (Show Source):
You can put this solution on YOUR website! 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.
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