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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

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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