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Question 76569: While finding the amount of seed needed to plant his three square wheat fields, Hank observed that the side of one field was 1 kilometer longer than the side of the smallest field and that the side of the largest field was 3 kilometers longer than the side of the smallest field. If the total area of the three fields is 38 square kilometers, then what is the area of each field?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! While finding the amount of seed needed to plant his three square wheat fields, Hank observed that the side of one field was 1 kilometer longer than the side of the smallest field and that the side of the largest field was 3 kilometers longer than the side of the smallest field. If the total area of the three fields is 38 square kilometers, then what is the area of each field?
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Let x = side of the smallest square field; Area = x^2
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Let (x+1) = side of the medium field; Area = (x+1)^2
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Let (x+3) = side of the larger field; Area = (x+3)^2
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x^2 + (x+1)^2 + (x+3)^2 = 38;
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x^2 + (x^2 + 2x + 1) + (x^2 + 6x + 9) = 38; FOILed (x+1)^2 and (x+3)^2
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x^2 + x^2 + x^2 + 2x + 6x + 1 + 9 - 38 = 0; Group like terms
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3x^2 + 8x - 28 = 0; a quadratic equation
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(3x + 14)(x - 2) = 0; factored
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3x = -14
x = -14/3; not the the solution
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x = +2 kilometer, the side of the small field
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Med field side = 2 + 1 = 3 km
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Large field side = 2 + 3 = 5 km
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Check 2^2 + 3^2 + 5^2 =
4 + 9 + 25 = 38
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Did this make sense to you? Any questions?
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