A hall, whose length is 16 m and the breadth is twice its height, takes 168 m of paper with 2 m as its width to cover its four walls. The area of the floor is :

Answer: Option C

Let the height of the room be x metres
Then, breadth of the room = (2x) metres
Area of 4 walls :
$$\begin{array}{rl}& =\left[2\left(16+2x\right)\times x\right]m^2\\ & =\left(32x+4x^2\right)m^2\end{array}$$
$$\begin{array}{rl}& \therefore \left(32x+4x^2\right)=168\times 2\\ & \Rightarrow x^2+8x-84=0\\ & \Rightarrow x^2+14x-6x-84=0\\ & \Rightarrow x\left(x+14\right)-6\left(x+14\right)=0\\ & \Rightarrow \left(x+14\right)\left(x-6\right)=0\\ & \Rightarrow x=6\end{array}$$
Area of the floor :
= (16 × 12) m²
= 192 m²