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 143980: 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 problem is included in a chapter that has factoring equations and the Pythagorean theorem. I would appreciate any help - thanks!
Answer by vleith(2517) (Show Source):
You can put this solution on YOUR website!
let x be the side of the smallest field. It's area is x^2
The next field is (x+1)^2 = x^2 + 2x + 1
The bi field is (x+3)^2 = x^2 + 6x + 9
The total is 38

x = -14 or x =2
Since the field cannot be less than 0, x must be 2.
the next field is 3 and the big one is 5.
Does 5^2 + 3^3 + 2^2 = 38?