6th Class Mathematics Sample Paper Mathematics Sample Paper-6

  • question_answer The floor of a room is 8 m 96 cm long and 6 m 72 cm broad. Find the minimum number of square tiles of the same size needed to cover the entire floor.

    Answer:

    Given, length of the floor = 8 m 96 cm \[=8\times 100\text{ }cm+96\text{ }cm\] [\[\therefore \]\[1\,m=100\text{ }cm\]] \[=800+96\text{ }cm\] \[=896\text{ }cm\] and breadth of the floor \[=6m\text{ }72cm\] \[=6\times 100\text{ }cm+72\text{ }cm\] [\[\therefore \]  \[1\,m=100\text{ }cm\]] \[=672\text{ }cm\] Now, size of the square tile = HCF of 896 and 672 Prime factorization of 896 and 672

    2 896
    2 448
    2 224
    2 112
    2 56
    2 28
    2 14
    7 7
    1
    2 672
    2 336
    2 168
    2 84
    2 42
    3 21
    7 7
    1
    \[896=2\times 2\times 2\times 2\times 2\times 2\times 2\times 7\] \[672=2\times 2\times 2\times 2\times 2\times 3\times 7\] Common factors of 896 and 672 \[=2\times 2\times 2\times 2\times 2\times 7\] \[=224\] \[\therefore \] Minimum no. of square tiles                  \[\text{=}\frac{\text{Area}\,\,\text{of}\,\,\text{floor}}{\text{Area}\,\,\text{of}\,\,\text{square}\,\,\text{tile}}\]                  \[=\frac{896\times 672}{224\times 224}\] [\[\therefore \]  area of square\[={{(side)}^{2}}\]]                  \[=\frac{896\times 3}{224}\]                  \[=4\times 3=12\]


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