Representation:

x = measurement of width

2x - 6 = measurement of length

108 = area

Working Equation: (x)(2x - 6) = 108

Solution:

(x)(2x - 6) = 108

2x² - 6x = 108

2x² - 6x - 108 = 108 - 108

2x² - 6x - 108 = 0 <--- Factor the equation

2(x + 6)(x - 9) = 0

x + 6 = 0 or x - 9 = 0

x = -6 or x = 9

Since this is a word problem, a negative answer is not applicable. Therefore, we must choose the positive answer, which is x = 9

ANSWER: The width of the rug is 9 cm.