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.
9
4
thare is only 1 differint rectangles
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.
18x1 9x2 6x3
3
9
13
The area doesn't tell you the perimeter. There are an infinite number of different shapes and different dimensions that all have the same area but different perimeters. Here are a few 1/4-acre rectangles, and their perimeters: 90-ft x 121-ft . . 422-ft 30' x 363' . . . . . 786' 15' x 726' . . . . 1,482' 10' x 1,089' . . . 2,198' 6' x 1,815' . . . . 3,642' 2' x 5,445'. . . . 10,894'
Infinite amounts.
technically the number is infinite
4
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.
thare is only 1 differint rectangles
5
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.