The perimeter of a standard-sized rectangular rug is 36 is 36 ft. the length is 2 ft longer than the width. find the dimensions

The formula for the perimeter of a rectangle is P = 2L + 2W, where L is the length and W is the width. Because we don't know either the length or the width we can't solve the problem...too many unknowns.  BUT we do have some information that will help with this problem.  We are told that the length is 2 feet longer than the width, so we can use that: L = W+2.  Now we can make the substitution into the formula along with the value for the perimeter that was given to us: 36=2(W+2) + 2W, and 36 = 2W + 4 + 2W; 36 = 4W + 4; 32 = 4W and W = 8.  Now go back to where you said that the length is 2 feet longer than the width.  If the width is 8, then 8+2 = 10 for the length.