How many rectangles have an perimeter of 18 units?

Answer 1

Perimeter = 18 = 2L + 2W

9 = L + W

Graph it, it's an infinitely long line with intercepts (0,9) and (9,0)

any point on the line segment between the two intercepts is a solution, there are an infinite number of rectangles with perimeter 18

If you want to limit the rectangles to integer length and width then

W L

8 by 1

7 by 2

6 by 3

5 by 4

4 by 5

3 by 6

2 by 7

1 by 8

are the only 8 possible rectangles

or just 4 if count the 2nd half as equivalent to the first half. 1 x 8 the same as 8 x 1, etc.