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.
Chat with our AI personalities
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