Hector needs 84 feet of fencing to enclose his rectangular garden. the length of his garden is 12 feet less than twice its width. what is the width of his garden?

The problem statement gives rise to two equations. One is for the relation of length and width to the perimeter.
  P = 2(L +W)
  84 = 2(L +W)
  42 = L +W

And the other is for the relation between length and width.
  L = 2W -12

Substituting this last expression for L into the equation from the perimeter relationship, we get
  42 = (2W -12) +W
  54 = 3W . . . . . . . . collect terms, add 12
  18 = W . . . . . . . . .. divide by 3

The width of Hector's garden is 18 ft.


If we wish, we can go on to find the length of the garden.
  L = 2W -12 = 2*18 -12 = 24 . . . . feet