Question 162784
let s = side of smallest field.
let m = side of middle field.
let l = side of largest field.
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s = s kilometers
m = s+1 kilometers
l = s+3 kilometers
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total area of all 3 fields is 38 square kilometers.
s^2 + m^2 + l^2 = 38
since m = s+1 and l = s+3, substitute in equation to get
s^2 + (s+1)^2 + (s+3)^2 = 38
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this becomes
s^2 
+ s^2 + 2s + 1
+ s^2 + 6s + 9
= 38
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this becomes
3s^2 + 8s + 10 = 38
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subtracting 38 from both sides of equation and it becomes
3s^2 + 8s - 28 = 0
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factoring this equation yields
(3s+14) * (s-2) = 0
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s = 2 was substituted in original equation of s^2 + (s+1)^2 + (s+3)^2 = 38 and is good.
s = -14/3 was rejected because the side of the field can't be negative.  it was substituted in the original equation and it worked, but it can't be used.
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smallest field is 2 kilometers per side.
middle field is 3 kilometers per side.
largest field is 5 kilometers per side
2^2 + 3^2 + 5^2 = 4 + 9 + 25 = 38 square kilometers.
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equation is satisfied.
area of the smallest field is 4.
area of the middle field is 9.
area of the largest field is 25.