Question 154467This question is from textbook elementary and intermediate algebra
: I can't figure thisone out please help. #78. 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?
Thanks you
This question is from textbook elementary and intermediate algebra
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 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.
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