The cost of preparing the walls of a room 12 m

The cost of preparing 4 walls of a room whose length is $12 \mathrm{~m}$ is $\mathrm{Rs} 340.20$ at a rate of $\mathrm{Rs} 1.35 / \mathrm{m}^{2}$.

$\therefore$ Area of the four walls of the room $=\frac{\text { total cost }}{\text { rate }}=\frac{\mathrm{Rs} 340.20}{\mathrm{Rs} 1.35}=252 \mathrm{~m}^{2}$

Also, the cost of matting the floor at 85 paise $/ \mathrm{m}^{2}$ is Rs $91.80$.

$\therefore$ Area of the floor $=\frac{\text { total cost }}{\text { rate }}=\frac{\mathrm{Rs} 91.80}{\mathrm{Rs} 0.85}=108 \mathrm{~m}^{2}$

Hence, breadth of the room $=\frac{\text { area of the floor }}{\text { length }}=\frac{108}{12}=9 \mathrm{~m}$

Suppose that the height of the room is $\mathrm{h} \mathrm{m} .$ Then, we have :

Area of four walls $=2 \times($ length $\times$ height $+$ breadth $\times$ height $)$

$\Rightarrow 252=2 \times(12 \times \mathrm{h}+9 \times \mathrm{h})$

$\Rightarrow 252=2 \times(21 \mathrm{~h})$

$\Rightarrow 21 \mathrm{~h}=\frac{252}{2}=126$

$\Rightarrow \mathrm{h}=\frac{126}{21}=6 \mathrm{~m}$

$\therefore$ The height of the room is $6 \mathrm{~m}$.