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 :

Solution(By Examveda Team)

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