A room of the hall is such that the ratio of the height of the room to its semi perimeter is \[\mathbf{6}:\mathbf{10}\] and the cost of wall paper to cover the walls of the room is Rs. 1700, when the width of the paper is 100 cm at the rate of Rs. \[\mathbf{10}\text{ }\mathbf{per}\text{ }\mathbf{mete}{{\mathbf{r}}^{\mathbf{2}}}\], except the door and window whose area is \[\mathbf{40}\text{ }{{\mathbf{m}}^{\mathbf{2}}}\]. The height of the room is:

• A. \[2\sqrt{6}~m\]                
• B.                   \[6\sqrt{1.75}~m\]
• C. \[4\sqrt{6}~m\]               
• D.        \[5~\sqrt{6}\,m\]
• E. None of these