Answer:

Step-by-step explanation:
The area of the rectangular rug is given by this equation:

The area must be a number greater than 0 since a negative area, or an area equal to 0 wouldn't have much sense. So:

Let's find the roots of this equation using the quadratic formula:

Now, let's evaluate the area for
for example r=1.05:

The result is greater than zero, so for
the values make sense.
Now let's evaluate the area for
for example r=0.5 and r=-0.7:

The result is less than zero, so for
the values don't make sense.
Now, let's evaluate the area for
for example r=-1:

The result is greater than zero, so for
the values make sense
However, since negative values of r wouldn't make much sense (I never heard about of -8 inches for example) the possible dimensions of the rug are just:
