This problem is about the area of a square.
Notice that the mat has square form, this means its area is defined by
![A=l^2](https://img.qammunity.org/2023/formulas/mathematics/college/u8m4ktzz90c2ymvqwncx2eqjofo7ic02t9.png)
Where l is the length of each side.
Now, to find the length of the side, we just need to use the formula above and replace the area with its number 81
![81=l^2](https://img.qammunity.org/2023/formulas/mathematics/college/eraiuh038h1aad9fpxact7x9cqr3qihtv6.png)
We solve for l
![l=√(81)=9](https://img.qammunity.org/2023/formulas/mathematics/college/w9fptb1a8vwz147xkm0cttciy4ba0hvoy1.png)
Therefore, the length of the side is 9 feet.