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Any number greater than 24.56 cm (approx).

A circle, with a perimeter of 24.56 cm has an area of 48 cm2. A polygon with very many sides will approximate the circle.

At the other extreme,

suppose L ≥ 4*sqrt(3) = 27.71 cm

and let W = 48/L

Then the area of a rectangle with length L and width W is L*W = L*(48/L) = 48 cm2. The perimeter is 2*(L+48/L) cm.

There is no maximum value for L and so, by making the rectangle thinner and longer, the perimeter can be increased to any number of your choosing.

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