# SOLUTION: A rug placed in a 10 ft x 12 ft room covers two-thirds of the floor area and leaves a uniform strip of bare floor around teh edges. Find the dimensions of the rug. I dont need th

Algebra ->  Algebra  -> Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A rug placed in a 10 ft x 12 ft room covers two-thirds of the floor area and leaves a uniform strip of bare floor around teh edges. Find the dimensions of the rug. I dont need th      Log On

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 Click here to see ALL problems on Linear Equations And Systems Word Problems Question 152282: A rug placed in a 10 ft x 12 ft room covers two-thirds of the floor area and leaves a uniform strip of bare floor around teh edges. Find the dimensions of the rug. I dont need the answer, just the step-by-step process.Answer by nerdybill(6963)   (Show Source): You can put this solution on YOUR website!The important thing is to draw a diagram. Label all the information provided. . Let x = width of strip between the edge of the rug and wall . The room is 10 by 12 feet. . Therefore the rug must be: (10-x) by (12-x) . The area of the rug is equals to 2/3 of the room: (10-x)(12-x) = 2/3(10*12) (10-x)(12-x) = 2/3(120) (10-x)(12-x) = 2(40) (10-x)(12-x) = 80 120-10x-12x+x^2 = 80 120-22x+x^2 = 80 x^2-22x+120 = 80 x^2-22x+40 = 0 (x-20)(x-2) = 0 . x = {2,20} . Therefore the rug is: 10 feet by 8 feet