The length of a rectangular pitch is 30 m more than its breadth. Its area is 18,271 m\(^2\). Its breadth (in m) is:

Let the breadth of the rectangular pitch be $x$ m.

Then, length = $(x + 30)$ m

Given area = $18,271 \text{ m}^2$

So,

$x(x + 30) = 18271$

$x^2 + 30x - 18271 = 0$

Now factorise:

$x^2 + 30x - 18271 = 0$

$x^2 + 151x - 121x - 18271 = 0$

$x(x + 151) - 121(x + 151) = 0$

$(x + 151)(x - 121) = 0$

$x = 121$ (breadth cannot be negative)

Therefore, the breadth of the rectangular pitch is

Answer = 121  m