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10th Class Mathematics Mensuration Question Bank Mensuration

  • question_answer
    The length and breadth of a room are in the ratio of 3:2. Its height is equal to half of its length. If the cost of carpeting the floor at Rs. \[\text{4}.00\text{ per }{{\text{m}}^{\text{2}}}\]is Rs, 216, then the area of four walls (in\[{{\text{m}}^{\text{2}}}\]) is

    A)  135                   

    B)         140

    C)  125                       

    D)  120

    Correct Answer: A

    Solution :

     Let the length and breadth be \[2x\] and \[3x\] respectively. Then, floor area \[=6{{x}^{2}}\,sq.m.\] Cost of flooring at the rate of \[Rs.\,4.00\,per\,{{m}^{2}}\]                                                 \[=Rs.\,216\] \[\therefore \]  \[6{{x}^{2}}\times 4=216\] or            \[{{x}^{2}}=9\] or            \[x=3\] \[\therefore \]                  Length \[=3x=9m\] Breadth \[=2x=6m\] and     Height \[=\frac{1}{2}\times Length=4.5m\] \[\therefore \]  Area of four walls \[=2[length\times height+breadth\times heigth]\] \[=2[9\times 4.5+6\times 4.5]=135\,{{m}^{2}}\]


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