Subject: General Aptitude · Chapter: Area · Exam: · Marks: · Difficulty:
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
(a)$96 \mathrm{m}^{2}$
(b)$190 \mathrm{m}^{2}$
(c)$192 \mathrm{m}^{2}$
(d)$216 \mathrm{m}^{2}$
Answer
Answer (as printed): C
Explanation
Let the height of the room be $x$ metres. Then, breadth of the room $=(2 x)$ metres. Area of 4 walls $=[2(16+2 x) \times x] \mathrm{m}^{2}=\left(32 x+4 x^{2}\right) \mathrm{m}^{2}$. $$\begin{aligned} & \therefore 32 x+4 x^{2}=168 \times 2 \Rightarrow x^{2}+8 x-84=0 \\ & \Rightarrow x^{2}+14 x-6 x-84=0 \Rightarrow x(x+14)-6(x+14)=0 \\ & \Rightarrow(x+14)(x-6)=0 \Rightarrow x=6 \end{aligned}$$ Area of the floor $=(16 \times 12) \mathrm{m}^{2}=192 \mathrm{m}^{2}$