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Hi,
The area of the Room is 55 square feet the length is 6 feet longer than the width 
area = l*w = (x+6)x
(x+6)x = 55ft^2
x^2 + 6x - 55 = 0
(x+11)(x-5) = 0
x = 5, throwing out negative solution for unit of measurement
width is 5 and length is 11