SOLUTION: Please help. 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 s

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Question 175648: Please help.
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 thatn 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 ankor@dixie-net.com(22740) (Show Source):
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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.
:
let x = side of the smallest square
area = x^2
:
(x+1) = side of the next largest square
area = (x+1)^2 = (x^2 + 2x + 1)
:
(x+3) = side of the largest square
area = (x+3)^2 = (x^2 + 6x + 9)
:
The sum of the three areas:
x^2 + (x^2 + 2x + 1) + (x^2 + 6x + 9) = 38
group like terms
x^2 + x^2 + x^2 + 2x + 6x + 1 + 9 - 38 = 0
Combine like terms
3x^2 + 8x - 28 = 0
Factors to:
(3x + 14)(x - 2) = 0
The positive solution
x = 2 km side of the smallest field
then
2 + 1 = 3 km is the side of the next largest
and
2 + 3 = 5 km is the side of the largest field
;
;
Check solution:
2^2 + 3^2 + 5^2 =
4 + 9 + 25 = 38; confirms our solutions