The longest side can't be 10 meters because 10 is not an odd integer.
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Perimeter = Side1 + Side2 + Side3
Side2 = Side1 + 2 (next odd integer above Side1)
Side3 = Side1 + 4 (next odd integer above Side2)
Perimeter = Side1 + Side1 + 2 + Side1 + 4
Perimeter = 3*Side1 + 6
Perimeter = 21
3*Side1 + 6 = 21
3*Side1 = 15
Side1 = 5
Side2 = 7
Side3 = 9
Check: 5 + 7 + 9 = 21, good.
Answer: The longest side is 9 meters.