SOLUTION: winter wheat: while finding the amount of seed needed to plant to plant his three square wheat fields, hank observed that the side of one field was 1 kilometer longer than the side

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Question 169378: winter wheat: while finding the amount of seed needed to plant 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 Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
lets call the small field a. So the one field is a+1 and the largest field is a+3. remember these are square fields
:
so we have a%5E2%2B%28a%2B1%29%5E2%2B%28a%2B3%29%5E2=38 distribute the left side
:
a%5E2%2Ba%5E2%2B2a%2B1%2Ba%5E2%2B6a%2B9=38 now combine like terms
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3a%5E2%2B8a%2B10=38 subtract 38 from both sides
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3a%5E2%2B8a-28=0 now quadratic equation gives us
a=2 and -4.6666....so throw out the negative and we have
:
highlight%28a=2%29 smallest field
highlight%28a%2B1=3%29 middle field
highlight%28a%2B3=5%29 large field