I’ve been racking my (admittedly limited) brains trying to figure out a way to solve this homework problem. There doesn’t appear to be any problems similar to it in my textbook.
I know the total area of the room must be twice the dimensions of the rug (4*6=48m^2). But after that I’m drawing a blank.
The key lies in the strips of bare floor being uniform in width. Let’s call this width w. Can you express the dimensions of the room in terms of this w?
Since it’s homework, I’ll give you a couple of nudges in the right direction, rather than answer outright.
The key is that the strip of bare floor around the rug is uniform, which means you can define it as a single variable–call it x.
Use that to write an equation describing the area of the room.
You should be able to use arithmetic to work that equation around into a (hopefully) familiar-looking form. Once you’ve got that, solve for x. (Remember that x isn’t your final answer, though.)
Another nudge. The area of the “strip” is equal to the area of the rug.
Heh I just guessed factors of 48…it can only be one possible pairing.
Good luck showing your work on that one. 
Can I piggyback on this thread to ask my own algebra question? This isn’t homework, except insofar as it’s self-assigned homework.
In my finance exercise book, the formula for present value annuity factor is written in two equivalent forms (I’ll do my best with the notation here), but I can’t figure out how one can be turned into the other:
1/r*( 1 - 1/(1 + r)^t) = ( (1 + r)^t - 1 ) / ( r*(1 + r)^t )
(ETA: r is rate and t is time, if it makes any difference)
The furtherest I can get is taking the part to the left of the equals sign and multiplying 1/r times 1 and by -1/(1 + r)^t, which gives me (I think)
1/r - r / r*(1 + r)^t
(if there’s a better way to do this notation, please tell me how!)
Anyway, it’s been 20 years since I had to do algebra, and I’m asking mainly out of curiousity – not grade dependent. If any math types would be amused taking a spare moment to figure out, I’d be much obliged!
Maybe you should start your own thread! you’re delaying someone’s HW assignment! 
I’m guessing your equations should really read:
(1/r)( 1 - 1/(1 + r)^t) = ( (1 + r)^t - 1 ) / ( r(1 + r)^t )
Start with the right hand side:
R
Wow, thanks! That makes sense – and confirms my sneaking suspicion that there was a typo in my book. (The exponent in the numerator is given as “t”, not “t - 1”)
Much appreciated!
Oops, mistake!
The book I’m sure had proof readers, I didn’t.
numerator needs to be (1+r)^t -1 , not t-1 for this to work.
2 * 6 * 4 = (6 + x) * (4 + x)
Now it makes even more sense! Yeah . . . that’s the ticket . . .
My brain just shuts down sometimes when confronted with exponents. But I can see now what you’re doing is multiplying the 1/r by [ (1 + r)^t / (1 + r)^t ] in order to make the denominator the same as what’s on the right side of the minus sign, so you can bring it all together.
Thanks again!
Wouldn’t it be 2x, since the strip is uniform around the rug and you have x amount on each side and end?
It’s been… ah, a ‘little while’ since I’ve done this.
That just makes it more complex to solve. Say that I have a room that’s 7’x5’ and a rug that is 5’x3’. If I put the rug in one corner, then there’s a 2’ gap running along two sides. If I center the rug, there’s a 1’ gap running along all four sides. Either way, the dimensions of the room and the rug don’t change. Since it’s easier to solve for the rug being in the corner, you might as well just solve for that.