Question 772698
Drawing a picture may be helpufl (but I have not included one here.)


Let the length of the room be x and the width of the room be y.
According to given, {{{highlight(x=2y)}}}.


Placement of the carpet is done in order to form a bare area 3 meters around the carpet.
Carpet length is {{{x-2*3=x-6}}}
Carpet width is {{{y-2*3=y-6}}}
We were also told that carpet length & width are in same ratio as that of the room, so
{{{highlight(x-6=2(y-6))}}}


The highlighted equations give a system in the two variables, x and y.  The equations are only for lengths, so these are linear equations.  Solve the system for x and y and you can compute both the area of the room, and the area of the carpet.  You will want to perform a couple of operations on the carpet highlighted equation before the fully handle the two equations as a system; you would want the equations in as much the same format as possible before finishing to find x and y.