MathematicsWhat is the minimum number of identical square tiles required to completely cover a floor of dimensions 8 m 70 cm by 6 m 38 cm?

What is the minimum number of identical square tiles required to completely cover a floor of dimensions 8 m 70 cm by 6 m 38 cm?


  1. A
    143
  2. B
    165
  3. C
    187
  4. D
    209 

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    Solution:

    Floor dimensions are listed as 8m 70cm x 6m 38cm. We know that 1 m is 100 cm. We will use this information to convert measurements from m to cm. So we have a floor length of 8 m 70 cm, which is 800 cm + 70 cm, so 870 cm. The width of the floor is given as 6 m 38 cm, i.e. 600 cm + 38 cm, which adds up to 638 cm.
    Now let's calculate the floor area. The length and width of the floor is given to us. So we use the formula for the area of ​​a rectangle to calculate the area of ​​the floor. The area of ​​the rectangle is given by . By substituting the length and width values, we get
    Area of the floor = 870×638 c m 2 =555060 c m 2   Further assume that the side of the isosceles is . The area covered by one such square will therefore be . To find the number of squares that cover the floor, we need to consider the following ratio:
    number of squares : area covered  
    So we have  1: x 2   and  n:555060  , where  n  n is the number of square tiles required to cover the floor.
    Therefore, we get that  n× x 2 =555060  .
    Since we do not know the side of the square, we will eliminate options to find the correct Ans.
    If we substitute  n=143   which is option (a), we get  x 2 = 555060 143 =3881.5385  . As this does not look like a perfect square, we will eliminate this option.
    Next, we will substitute  n=165  which is option (b). We have  x 2 = 555060 165 =3364   and hence, we get  x=58 cm  . That seems like the best option.
    We can also rule out options (3) and (4) because dividing the floor area by the numbers given in these options gives us decimal values.
    So the number of square tiles with a side length of 58 cm to cover the floor is 165.
     
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