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?
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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
and 
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?