Question 836645
The solution steps for just the arithmetic is the easier part.  The hard part is to analyze and develop the initial equation to solve.


Matt wants the rug to fit inside the {{{12*15*ft^2}}} room, and leave the uniform unrugged strip, and the rug should cover {{{108*ft^2}}}.  Let the width of the unrugged strip around the rug be w.  Starting from the {{{12*15}}} room, removing the area of the empty strip should leave the {{{108*ft^2}}} area.


One dimension of the rug is (12-2w); and the other dimension of the rug is (15-2w).  Use a figure, or picture if necessary to understand this.  Once you understand, then you're ready to continue.


READY?


{{{RugArea=highlight((12-2w)(15-2w)=108)}}}
and the rest is left for you to do.  Solve for w.  Use w to get the rug dimensions.