Answer:
The dimensions should the rug have: length = 25 feet and width of 14 feet.
Step-by-step explanation:
Dimension of the room is 20 ft wide and 31 ft long
Area of rug purchased by Cynthia Besch = 
Suppose she leave strip of floor which is x ft thick.
Length of the rug= l = (31-x) ft
Width of the rug= w = (20-x) ft
Area of the rug,A = l × w






x = 45 , 6
x = 6 (accept), x= 45 ,(reject, larger than length of the room )
Length of the rug= l = (31-x) ft = 31 - 6 ft = 25 ft
Width of the rug= w = (20-x) ft = 20 - 6 ft = 14 ft