Question 167953: Winter wheat. 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 stanbon(75887)   (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 side of smallest field be "x" km ; Smallest area = x^2 km^2
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Another field has side = "x+1" km ; area = (x+1)^2 km2
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Largest field has side = "x+3" km ; area = (x+3)^2 km^2
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EQUATION:
x^2 + (x+1)^2 + (x+3)^2 = 38
x^2 + x^2 +2x + 1 + x^2 + 6x + 9 = 38
3x^2 + 8x -28 = 0
(3x + 14)(x-2) = 0
x = -14/3 or x = 2
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Cheers,
Stan H.
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