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Infinitely many.

Select any number, L, such that 12 < L < 24. Let W = 24 - L. Then a rectangle with sides of length L cm and width W cm will have a perimeter of 48 cm. And since the choice of L was arbitrary, there are infinitely many possible values of L and thence infnitely many rectangles.

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Q: How many different rectangles have a perimeter of 48cm?
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