SOLUTION: The area of a rectangular lot 80m by 100m is to be increased by 4000m^2. The length and the width will be increased by the same amount. What are the dimensions of the larger lot?
Question 520392: The area of a rectangular lot 80m by 100m is to be increased by 4000m^2. The length and the width will be increased by the same amount. What are the dimensions of the larger lot? Answer by oberobic(2304) (Show Source):
You can put this solution on YOUR website! Area = Length * Width
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A = 80 m * 100 m
A = 8000 m^2
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The area is increased by 4000...
A = 8000 + 4000 m^2
A = 12000
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L and W will be increased by the same amount.
What are the new dimensions?
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x = the amount of increase
80+x = new dimension
100+x = new dimension
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(80+x)(100+x) = 12000
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use FOIL
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8000 +80x +100x + x^2 = 12000
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rearrange
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x^2 + 180x + 8000 -12000 = 0
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x^2 +180x -4000 = 0
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factor
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(x+200)(x-20) = 0
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check using FOIL
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x^2 -20x +200x -4000 = 0
OK
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x = -200 or 20
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Negative length and width are nonsense, so x = 20 is the only reasonable solution.
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Re-read the question to be sure you answer it.
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Answer: The dimensions of the new lot are 100 by 120 m.
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Always check your answer.
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100*120 = 12000 = 8000 + 4000
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Done.
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