SOLUTION: A rug placed in room 12 m long and 9 m wide covers half the floor area and leaves a uniform strip of bare floor around the edges. What are the dimnesions of the rug?

Question 76047: A rug placed in room 12 m long and 9 m wide covers half the floor area and leaves a uniform strip of bare floor around the edges. What are the dimnesions of the rug?
Answer by checkley75(3666) (Show Source): You can put this solution on YOUR website!
(12-2X)(9-2X)=(12*9)/2
108-18X-24X+4X^2=108/2
4X^2-42X+108=54
4X^2-42X+108-54=0
4X^2-42X+54=0
(X-9)(4X-6)=0
X-9=0
X=9
4X-6=0
4X=6
X=6/4
X=1.5 FEET IS THE WIDTH OF THE BARE FLOOR WHICH EQUALS 1/2 OF THE FLOOR AREA.
PROOF
(12-2*1.5)(9-2*1.5)=(12*9)/2
(12-3)(9-3)=108/2
9*6=54
54=54

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