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?
Answer by jorel555(1290)   (Show Source):
You can put this solution on YOUR website! 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:
(6+2w)(4+2w)=48
24+20w+4w²=48
4w²+20w-24=0
w²+5w-6=0
(w+6)(w-1)=0
w=1 or -6
Throwing out the negative result, we get the width of the bare floor not covered by the rug to be 1 meter. ☺☺☺☺
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