Question 380768: 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! 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?
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Let the side of the smallest field be "x": Area = x^2
Side of middle field is "x+1": Area = (x+1)^2
Side of largest field is "x+3": Area = (x+3)^2
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Equation:
x^2 + x^2+2x+1 + x^2+6x+9 = 38
----
3x^2 + 8x + 10 = 38
---
3x^2 + 8x - 18 = 0
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Positive solution:
x = 1.456
---
x^2 = 2.12
(x+1)^2 = 2.456^2 = 6.03
(x+3)^3 = 4.456^2 = 19.86
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Cheers,
Stan H.
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