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put this solution on YOUR website!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
