Answer: Option C
Let the breadth and height of the room be b metres and h metres respectively.
Then, length of the room = (2b) metres
Area of the ceiling :
$$\eqalign{
& = \left( {2b \times b} \right)m \cr
& = \left( {2{b^2}} \right){m^2} \cr} $$
$$\eqalign{
& 2{b^2} = \frac{{5000}}{{25}} \cr
& 2{b^2} = 200 \cr
& {b^2} = 100 \cr
& b = 10 \cr} $$
So, length = 20 m, breadth = 10 m
Area of 4 walls :
$$\eqalign{
& = \left[ {2\left( {20 + 10} \right) \times h} \right]{m^2} \cr
& = \left( {60h} \right){m^2} \cr} $$
$$\eqalign{
& \therefore 60h = \frac{{64800}}{{240}} \cr
& \Rightarrow 60h = 270 \cr
& \Rightarrow h = \frac{{270}}{{60}} \cr
& \Rightarrow h = 4.5\,m \cr} $$