Question 154467
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 the side of the smallest field be "x" : Area of that field is x^2
Next largest field has side "x+1" : Area of that field is (x+1)^2
Largest field has side "x+3" : Area is (x+3)^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 + 10 = 38
3x^2 + 8x - 28 = 0
(3x+14)(x-2) = 0 
Positive solution:
x = 2 km
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smallest field area = 2^2 = 4 km^2
next largest: 3^2 = 9km^2
largst (x+3)^2 = 5^2 = 25km^2
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Cheers,
Stan H.