Are you sure this is the right question? to have an interval for such a question, we need an inequality. there's no inequality here.

let width = x

=> length = x + 2

=> Perimeter = 2x + 2(x + 2) = 44

=> 2x + 2x + 4 = 44

=> 4x + 4 = 44

=> 4x = 40

=> x = 10

so the width is 10 and the length is 12

so the rug is a 10 x 12 rug

EDIT: oh, the interval thing is for the second question, ok i'll do that...what is xl?