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
To find the different rectangles with an area of 32 square units, we need to consider the factor pairs of 32. The pairs are (1, 32), (2, 16), (4, 8), and their reverses, giving us the dimensions of the rectangles: 1x32, 2x16, 4x8, and 8x4. However, since the order of dimensions does not create a new rectangle, we have four unique rectangles: 1x32, 2x16, and 4x8. Thus, there are three distinct rectangles with an area of 32 square units.
4
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.
3
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You can make three rectangles. Remember that a square can also be a rectangle.5x14x23x3
Infinite amounts.
To find the different rectangles with an area of 32 square units, we need to consider the factor pairs of 32. The pairs are (1, 32), (2, 16), (4, 8), and their reverses, giving us the dimensions of the rectangles: 1x32, 2x16, 4x8, and 8x4. However, since the order of dimensions does not create a new rectangle, we have four unique rectangles: 1x32, 2x16, and 4x8. Thus, there are three distinct rectangles with an area of 32 square units.
technically the number is infinite
4
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.
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.