SOLUTION: 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

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Question 98207: 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 303795(602) About Me  (Show Source):
You can put this solution on YOUR website!
If the side of the small field is x then the next field will have a side of (x+1) and the last field has a side length of (x+3).
The total area of the three square fields will be
x%5E2%2B%28x%2B1%29%5E2%2B%28x%2B3%29%5E2
x%5E2%2Bx%5E2%2B2x%2B1%2Bx%5E2%2B6x%2B9
3x%5E2%2B8x%2B10
This is equal to the total area of 38 so
3x%5E2%2B8x%2B10=38
3x%5E2%2B8x-28=0
Factorise
%28x-2%29%283x%2B14%29=0
so x=2 or x=-4 2/3
Only a positive value makes sense
so the fields have a side length of 2, 3 and 5.
A check of these values shows the total area = 4 + 9 +25 = 38.