2. Questions Bank
  3. 8th Class
  4. Mental Ability
  5. Mensuration

8th Class Mental Ability Mensuration Question Bank Mensuration

  • question_answer
    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

    Correct Answer: B

    Solution :

    Explanation Option [b] is correct. Let the height of the room be 6x and its semi-perimeter be 10x. Area of the four wall \[=2~\times \,6x\times ~10x=120{{x}^{2}}\] Area of the paper needed \[=120{{x}^{2}}-40\] Length of the paper needed = \[\frac{120{{x}^{2}}-40}{1}\] Total cost of the paper \[=10~\times (120~{{x}^{2}}-40)=1700\] \[\Rightarrow 120\,{{x}^{2}}=210\Rightarrow \,{{x}^{2}}=\frac{210}{120}=1.75\Rightarrow x=\sqrt{1.75\,}m\] Therefore, height of the room is \[6\sqrt{1.75}\,m\].


You need to login to perform this action.
You will be redirected in 3 sec spinner