Let the length of the rectangular field be \(x\) meters. ∴ The breadth = \(\frac{2000}{x}\) meters ∴ The perimeter of the field = \(2\left(x + \frac{2000}{x}\right)\) meters According to the question: \[ 2\left(x + \frac{2000}{x}\right) = 180 \] \[ \Rightarrow \frac{x^2 + 2000}{x} = 90 \] \[ \Rightarrow x^2 + 2000 = 90x \] \[ \Rightarrow x^2 - 90x + 2000 = 0 \] \[ \Rightarrow x^2 - (50 + 40)x + 2000 = 0 \] \[ \Rightarrow x^2 - 50x - 40x + 2000 = 0 \] \[ \Rightarrow x(x - 50) - 40(x - 50) = 0 \] \[ \Rightarrow (x - 50)(x - 40) = 0 \] ∴ Either \(x - 50 = 0\) or \(x = 50\), Or \(x - 40 = 0\) or \(x = 40\) Since length is greater than breadth, ∴ The length of the field is 50 meters and the breadth is \(\frac{2000}{50} = 40\) meters.