A 4m by 6m rug covers half of the floor area of a room, and leaves a uniform strip of bare floor around the edges. What are the dimensions of the rooms?

1 Answer
Alan P.
Oct 6, 2015

The room is 6 m by 8 m

Explanation:

Room has an area of #2xx(4xx6) =48 m^2#
(since the rug covers half the area and the rug has an area of #4xx6 m^2#)

Let
#color(white)("XXX")L = # length of the room
#color(white)("XXX")W= # width of the room
#color(white)("XXX")s= #width of the uniform strip around the outside of the rug

#L=6+2s#
#W=4+2s#

Area of room
#LxxW = (6+2s)(4+2s)=48#

#rarr 24+20s+4s^2=48#

#rarr 4s^2+20s-24=0#

#rarr s^2+5s-6=0#

#rarr(s+6)(s-1)=0#

#rarr s=-6" or " s=1#

Since a strip width of #(-6)# is impossible
the strip has a width of #1# and
#L=6+2s = 8#
and
#W=4+2s = 6#

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