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.
9
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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.
thare is only 1 differint rectangles
Using all 13 squares, and not counting different orientations, only one.
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13
You can make three rectangles. Remember that a square can also be a rectangle.5x14x23x3
Assuming that you have to use all the rectangles, you have a few options:1x453x155x9Therefore, you are able to make three different rectangles.
Infinite amounts.
technically the number is infinite
Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. So, there are 5 rectangles with an area of 36 cm^2 is 5.
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Assuming the 12 squares are the same size, three. And three more if you count different orientations (swapping length and breadth) as different rectangles.
3 or 6, depending on whether rectangles rotated through 90 degrees are counted as different. The rectangles are 1x12, 2x6 3x4 and their rotated versions: 4x3, 6x2 and 12x1.
No. Many investigators have searched for such an example, but none have found it yet. According to all published research so far, two rectangles with the same area always have the same area. But the search goes on, in many great universities.