I need to find the length of the string, which is also the perimeter of the square. I can use the formula for the area of a square to find the length of one side of the square: A = s^2, where A is the area and s is the side length. Since A = 144, I can take the square root of both sides and get s = 12. The perimeter of the square is four times the side length, so P = 4s = 4(12) = 48. The string has a length of 48, and I want to use it to form a circle. I can use the formula for the circumference of a circle to find the radius of the circle: C = 2πr, where C is the circumference and r is the radius. Since C = 48, I can divide both sides by 2π and get r = 48 / (2π) = 24 / π. The area of the circle is given by the formula A = πr^2. I can plug in r = 24 / π and get A = π(24 / π)^2 = 576 / π. To round this to the nearest whole number, I can use a calculator or an approximation for π. I know that π is about 3.14, so I can divide 576 by 3.14 and get about 183.4. Rounding this to the nearest whole number, I get 183. 
A piece of string fits exactly once around the perimeter of a square whose area is 144.  Rounded to the nearest whole number, what is the area of the largest circle that can be formed from the piece of string?