What are all the possible dimensions of the area is 180 square feet?

Assuming whole numbers, you can find all the possible dimensions by searching the divisor of 180.

Those are: 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90 and 180

Then these are the possible dimensions:

x         y               area = x * y
feet    feet            feet^2

1        180            1 * 180 = 180

2        90              2 * 90 = 180

3        60              3 * 60 = 180

4        45             4 * 45 = 180

5        36             5 * 36 = 180

6        30             6 * 30 = 180

9        20             9 * 20 = 180

12      15             12 * 15 = 180

From there on, the numbers repeat just exchanging x and y.