This problem is about areas.
Assuming the rug has a square form, its area is defined by
[tex]A=l^2[/tex]Where l is the length of its side.
We know by given that the area is 64 square feet. Using this value, we find the side length
[tex]64=l^2\text{ }\rightarrow l=\sqrt{64}\rightarrow l=8[/tex]