document.write( "Question 1053123: A 4m by 6m rug covers half a floor area of a room and leaves a uniform strip of base floor around the edges. What are the dimensions of the room? \n" ); document.write( "

Algebra.Com's Answer #668495 by jorel555(1290) $\"\"$ $\"About$

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The rug covers half the floor area, so 4x6/(1/2)=48 sq.m. as the area of the floor. To leave a strip of uniform length around the rug, we get the length of the rug plus strip to be 6+2w, where w equals the width of the strip. The width of rug plus strip would be 4+2w. So:
\n" ); document.write( "(6+2w)(4+2w)=48
\n" ); document.write( "24+20w+4w²=48
\n" ); document.write( "4w²+20w-24=0
\n" ); document.write( "w²+5w-6=0
\n" ); document.write( "(w+6)(w-1)=0
\n" ); document.write( "w=1 or -6
\n" ); document.write( "Throwing out the negative result, we get the width of the bare floor not covered by the rug to be 1 meter. ☺☺☺☺ \n" ); document.write( "

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