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Lets assume that the length of the first side is x. That means the length of the second side is 2x+1, and the length of the third side is 2x+2. So if we add up all the side lengths, we get the perimeter, which is 21.
So x+2x+1+2x+2=21, which simplifies to 5x+3=21. Lets subtract 3 from each side to isolate 5x. 5x+3-3=21-3, 5x=18. Lets divide by 5 to find x, the length of the first side. 5x/5=18/5, x=3.6
So the lengths of the sides are 3.6 cm,8.2 cm, and 9.2 cm.