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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?

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143

165

187

209

answer is B.

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Detailed 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

A r e a o f t h e f l o o r = 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 = 555060143 = 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 = 555060165 = 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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