Question 499719
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.