Question 58655This question is from textbook
: While finding the amount of seed needed to plant his three square wheat fields, Hank observed that the side of one field was 1 KM 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?
This question is from textbook
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Hank observed that the side of one field was 1 KM 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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Assume that the fields are square:
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Let x = side of the small field:
Then (x+1) = side of the the medium field
and (x+3) = side of the largest field
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Add the areas of the 3 fields
x^2 + (x+1)^2 + (x+3)^2 = 38
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FOIL the 2nd * 3rd fields
x^2 + (x^2 + 2x + 1) + (x^2 + 6x + 9) = 38
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Remove brackets
x^2 + x^2 + 2x + 1 + x^2 + 6x + 9 = 38
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Group like terms, subtract 38 from both sides:
x^2 + x^2 + x^2 + 2x + 6x + 1 + 9 - 38 = 0
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3x^2 + 8x - 28 = 0; our old friend the quadratic equation
Factors to:
(3x + 14)(x - 2) = 0
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x = + 2 is the positive solution, ignore the negative solution
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Small field side = 2 km; Medium = 3Km; Large = 5 km
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Check it: 2^2 + 3^2 + 5^2 = 38
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