SOLUTION: A decorator plans to place a rug in a room 9 m by 12 m in such a way that a uniform strip of flooring around the rug will remain uncovered. If the rug is to cover half the floor s

Question 314175: A decorator plans to place a rug in a room 9 m by 12 m in such a way that a uniform strip of flooring around the rug will remain uncovered. If the rug is to cover half the floor space, what should the dimensions of the rug be?
Answer by checkley77(12844) (Show Source): You can put this solution on YOUR website!
9*12=108 YDS^2 IS THE ROOM AREA.
108/2=54 YDS^2 IS 1/2 THE ROOM AREA.
(9-2X)(12-2X)=54
108-24X-18X+4X^2=54
4X^2-42X+108-54=0
4X^2-42X+54=0
(2X-18)(2X-3)=0
2X-3=0
2X=3
X=3/2
X=1.5
(9-2*1.5)(12-2*1.5)=54
(9-3)(12-3)=54
6*9=54
54=54
THE RUG SHOULD BE 6 BY 9 YDS.

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