SOLUTION: REPOST (previously unanswered): 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 kilomet

Question 45723: REPOST (previously unanswered): 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 his smallest field and that the side of his largest field was 3 kilometers longer than the side of the smallest field. If the total area of all three fields is 38 square kilometers, then what is the area of each field? Please show all steps in work and final answers. Thanks
Answer by Fermat(127) (Show Source):
You can put this solution on YOUR website!
You have three fields, all square, so length = width.
Let x be the side length of the smallest square.
Then x+1 is the side length of another square.
And x+3 is the side length of the largest sqaure.
The area of the smallest square is x²
The area of the next square is (x+1)²
The area of the largest square is (x+3)²
Toatal sum of the fields areas is: A = x² + (x+1)² + (x+3)²
A = x² + x² + 2x + 1 + x² + 6x + 9
38 = 3x² + 8x + 10
3x² + 8x - 28 = 0
(3x + 14)(x - 2) = 0
x = -4 2/3, x = 2
Ignoring the negative side length,
x = 2 km
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Area of field1 = 2² = 4 square kilometres
Area of field2 = 3² = 9 square kilometres
Area of field3 = 5² = 25 square kilometres
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