jmc

Since the area of the square is 144, each side has length $\sqrt{144}=12$. The length of the string equals the perimeter of the square which is $4\times 12=48$. The largest circle that can be formed from this string has a circumference of 48 or $2\pi r=48$. Solving for the radius $r$, we get $r=\frac{48}{2\pi }=\frac{24}{\pi }$. Therefore, the maximum area of a circle that can be formed using the string is $\pi \cdot {\left(\frac{24}{\pi }\right)}^2=\frac{576}{\pi }\approx \boxed{183}$.