Answer
$3$ feet
Work Step by Step
The area of the whole rug can be found by the formula: $s^{2}$.
Substituting $6$ for $s$, we can get $6^{2}$, which equals $36$.
$25\%$ of $36$ is $\frac{1}{4}$ of $36$ or $36\div 4$ which equals $9$.
We know $9$ must be the area of the smaller inner square.
Using the formula above, $s^{2} = 9$, and by using square roots, we get $s = \pm 3$.
The length of a rug cannot be in the negatives, thus the length must be $3$ ft.
