The length of a hall is 3 metres more than its breadth

Let the breadth of the rectangular hall be $x$ metre.

Therefore, the length of the rectangular hall will be $(x+3)$ metre.

According to the question:

$x(x+3)=238$

$\Rightarrow x^{2}+3 x=238$

$\Rightarrow x^{2}+3 x-238=0$

$\Rightarrow x^{2}+(17-14) x-238=0$

$\Rightarrow x^{2}+17 x-14 x-238=0$

$\Rightarrow x(x+17)-14(x+17)=0$

$\Rightarrow(x+17)(x-14)=0$

$\Rightarrow x=-17$ or $x=14$

But the value $x$ cannot be negative.

Therefore, the breadth of the hall is 14 metre and the length is 17 metre.