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Suppose the rectangle has length L and width W where, as per convention, L >= W.

Now Perimeter = 22 = 2(L+W) so L+W = 11

L is a whole number >=11/2 ie L >= 6

Also, W>0 so L <= 10.

Thus L = 6,7,8,9,10 giving 5 possible areas for the rectangle.

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