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Infinitely many.

Let L be any number greater than or equal to sqrt(24) units.

and let B = 24/L

Then the area of the rectangle with length L units and breadth B units will be

L * B = L *24/L = 24 square units.

Since there are infinitely many possible values for L, there are infinitely many possible answers to the question.

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Q: How many possible rectangles with an area of 24 square units?
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