Question 99023
room area = 12*15=180 SQ. ft. (don't forget the word "sq.")
rug area = 108 SQ. ft. (don't forget the word "sq.")
Let x=amount of space between wall and rug.
(12-x)(15-x)=108
180-27x+x2=108
rearange and subtract 108 from each side: x^2-27x+72=0
Factor:(x-24)(x-3)=0
x=24 and x=3 
x=3 ft. must be the answer because x=24 is WAY too big.
Check:
12-3 * 15-3=9*12=108
Ed