$A$ prayer hall has a carpet area of $300 \ m^2$ with its length one metre more than twice its breadth. Find the dimensions of the prayer hall.

(N/A) Suppose the breadth of the hall is $x \ m$. Then,its length should be $(2x + 1) \ m$.
Now,the area of the hall $= \text{length} \times \text{breadth} = (2x + 1) \times x = (2x^2 + x) \ m^2$.
Given that the area is $300 \ m^2$,we have:
$2x^2 + x = 300$
$2x^2 + x - 300 = 0$
Applying the factorization method,we split the middle term:
$2x^2 - 24x + 25x - 300 = 0$
$2x(x - 12) + 25(x - 12) = 0$
$(x - 12)(2x + 25) = 0$
So,the roots of the equation are $x = 12$ or $x = -12.5$.
Since $x$ represents the breadth,it cannot be negative. Therefore,$x = 12$.
The breadth of the hall is $12 \ m$ and its length is $2(12) + 1 = 25 \ m$.