Question 499719: The rectangular floor of a new office building is 50 feet longer than it is wide. The building has 39,375 square feet of floor space. Find the dimensions of the floor of the new building
Answer by oberobic(2304)   (Show Source):
You can put this solution on YOUR website! Area of rectangle = Length * Width
Area = 39,375 (given)
Length = Width +50 (given)
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Substitute for L = W+50
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(W+50) * W = 39375
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Multiply through.
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W^2 + 50W = 39375
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Subtract 39375 from both sides
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W^2 + 50W -39375 = 0
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Factor, if possible.
You're looking for two factors of 39375 that have a difference of 50.
200^2 = 40000, so 200 is good place to start hunting.
225*175=39375! And they're 50 apart.
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(W+225)(W-175) = 0
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W = -225 or 175.
But a negative width is nonsense.
So, we think the width = 175.
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Substitute to find length.
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L = W+50
L = 175 + 50
L = 225
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Ordinarily, we check our work meticulously. But for this question, the answer has been handed to us "on a platter." From solving the factorization, we have 225 and 175, which total 39375 and are 50 apart.
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Answer:
Length = 225 ft.
Width = 175 ft.
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Note: always indicate your units.
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Done.
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