A rectangular garden is surrounded by a walk of uniform width. the area of the garden is 180 square yards. if the dimensions of the garden plus the walk are 16 yards by 24 yards, find the dimensions of the garden.

The area of the garden can be expressed as:

(16 - x) * (24 - x) = 180, x = width of walk

We can solve this:

384 + x² - 40x = 180

x² - 40x + 204 = 0

(x - 20) ² - 400 + 204 = 0

(x - 20) ² = 196

x - 20 = ±14

x = 20 ± 14

x = 6 or x = 34.

x cannot be 34 because then the walk would be wider than the garden, which is impossible so x = 6.

To find the dimensions of the garden, take 6 from the dimensions of the garden and the walk so:

16 - 6 = 10

24 - 6 = 18.

This makes sense because 18 * 10 = 180, the area of the garden.

You could also just do trial and error, which happens to be easier in this case but of course, it's not really ideal for all cases.