SOLUTION: 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 th

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Question 202753This question is from textbook
: 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? This question is from textbook

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = the side of the smaller field, then (x+1) = the side of the middle field and (x+3) equal the side of the largest field.
The three areas, which sum to 38 sq.km. are:
x%5E2%2B%28x%2B1%29%5E2%2B%28x%2B3%29%5E2++=+38 Simplify.
x%5E2%2B%28x%5E2%2B2x%2B1%29%2B%28x%5E2%2B6x%2B9%29+=+38
3x%5E2%2B8x%2B10+=+38 Subtract 38 from both sides.
3x%5E2%2B8x-28+=+0 Factor this trinomial.
%283x%2B14%29%28x-2%29+=+0 Apply the zero product rule.
3x%2B14+=+0 or x-2+=+0
3x+=+-14 or x+=+2 Discard the negative solution as the side must be a positive value.
highlight%28x+=+2%29
The area of the smallest field is x%5E2+=+4sq.km.
The area of the middle field is %28+x%2B1%29%5E2+=+9sq.km.
The area of the largest field is %28x%2B3%29%5E2+=+25sq.km.
4%2B9%2B25+=+38