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 of the floor

Question 171648This question is from textbook
: 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 of the floor space, what should the dimensions of the rug be? This question is from textbook

Answer by checkley77(12844) (Show Source): You can put this solution on YOUR website!
9*12=108 M^2 IS THE ROOM AREA.
(9-2X)(12-2X)=108/2
108-24X-18X+4X^2=54
4X^2-42X+108-54=0
4X^2-42X+54=0
(4X-6)(X-9)=0
4X-6=0
4X=6
X=6/4 OR 1.5 ANS.
PROOF:
(9-2*1.5)(12-2*1.5)=108/2
(9-3)(12-3)=54
6*9=54
54=54
ANS: THE RUG SHOULD BE 6 BY 9 METERS.
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