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Infinitely many.

Suppose the length of the rectangle if L feet where L is any number greater than sqrt(42) = approx 6.481 ft.

Let the width of the rectangle be W = 42/L feet.

Then its area is L*W = L*42/L = 42 sq ft

There are infinitely many possible values for L and so infinitely many rectangles.

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Q: How many rectangles of different dimensions have an area of 42 square feet?
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