24166

If we let one side of a rectangle be x and the other be y,

Area = xy
Perimeter = 2(x+y)

If they were to be equal,
xy = 2(x+y)
Dividing each side by xy,
[2(x+y)]/xy = 1
2x/xy + 2y/xy = 1
2/y + 2/x = 1

We can list possibilities from here on:
x=4,y=4
x=6,y=3
x=3, y=6
ect.

We can see that 2/y + 2/x = 1 has infinite solutions