Well first, let's figure out the diameter of the rug to see if it will fit in the room. We know that the circumference of the circle is πd. So we can solve for d from there (d is the diameter).
c = πd
50.24 = πd
50.24/π = d
d = about 16 ft
Knowing this, we know that the rug would not fit in the room and if it was centered, it would have a foot of rug sticking out from each wall. Therefore, the rug is two feet too wide.