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Infinitely many.

Let B be any number less than 6 cm, and let L = 12-B cm.

Then the perimeter of the rectangle, with length L and breadth B, is

2*[L+B] = 2*[(12-B)+B] = 2*12 = 24 cm.

There are infinitely many possible values for B, between 0 and 6 and so there are infinitely many possible rectangles.

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Q: How many rectangles have the perimeter of 24cm?
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