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# How many rectangles have the same area but different perimeters?

Updated: 12/8/2022

Wiki User

13y ago

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.

Wiki User

13y ago

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### How many rectangles have the same area and perimeter of 18?

thare is only 1 differint rectangles

### Do rectangles with the same area of 30 feet have the same perimeter?

They can, but not necessarily. Let's say we have a rectangle of 5x6 and another of 1x30. The areas of both are 30 square feet, but their perimeters are different. Perimeter of 5x6: 5+5+6+6=22 feet Perimeter of 1x30: 1+1+30+30=62 feet There are many more examples of this.

18x1 9x2 6x3