Infinitely many.
Select any number L, greater than sqrt(24) units an let B = 24/L.
then the rectangle with sides measuring L and B will have an area of L*B = L*24/L = 24 square units.
Also, B ≤ sqrt(24) ≤ L so that value of L gives a different rectangle. And, since there are infinitely many possible values for L, there are infinitely many possible rectangles.
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thare is only 1 differint rectangles
Infinitely many. Suppose the area of the rectangle is 100. We could create rectangles of different areas: 100x1 50x2 25x4 20x5 10x10 However, the side lengths need not be integers, which is why we can create infinitely many rectangles. Generally, if A is the area of the rectangle, and L, L/A are its dimensions, then the amount 2(L + (L/A)) can range from a given amount (min. occurs at L = sqrt(A), perimeter = 4sqrt(A)) to infinity.
Using all 13 squares, and not counting different orientations, only one.