<PRE><B>Question 152282</B>
The important thing is to draw a diagram.  Label all the information provided.
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Let x = width of strip between the edge of the rug and wall
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The room is 10 by 12 feet.
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Therefore the rug must be:
(10-x) by (12-x)
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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
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x = {2,20}
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Therefore the rug is:
10 feet by 8 feet</PRE>