Question

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?
(a) 143
(b) 165
(c) 187
(d) 209

Answer 1

Hint: The measurements of the floor are given in m and cm. So, we will convert the measurements from m into cm. Then we will find the area of the floor that needs to be covered. We will use the formula for the area of a rectangle. We will assume some side length for the square tiles and use it to divide the area of the floor by the area of one such square. This will give us the number of squares that will be required.

Complete step-by-step answer:
The measurements of the floor are given as 8 m 70 cm by 6 m 38 cm. We know that 1 m is 100 cm. we will use this information to convert the measurements from m into cm. So we have the length of the floor to be 8 m 70 cm, which is 800 cm + 70 cm, that is 870 cm. The breadth of the floor is given as 6 m 38 cm, that is 600 cm + 38 cm which adds up to 638 cm.
Now, we will calculate the area of the floor. The length and breadth of the floor is given to us. So we will use the formula for the area of the rectangle to calculate the area of the floor. The area of the rectangle is given by $A=l\times b$. Substituting the values of length and breadth, we get
$\begin{align}
  & \text{Area of the floor = 870}\times \text{638 c}{{\text{m}}^{2}} \\
 & =555060\text{ c}{{\text{m}}^{2}}
\end{align}$

Next, let us assume the side of the identical squares to be $x\text{ cm}$. So, the area covered by one such square will be ${{x}^{2}}\text{ c}{{\text{m}}^{2}}$. So, to find the number of squares that cover the floor, we have to consider the following ratio,
$\text{number of squares : area covered}$
So we have $1:{{x}^{2}}$ and $n:555060$, where $n$ is the number of square tiles required to cover the floor.
Therefore, we get that $n\times {{x}^{2}}=555060$.
Since we do not know the side of the square, we will eliminate options to find the correct answer.
If we substitute $n=143$ which is option (a), we get ${{x}^{2}}=\dfrac{555060}{143}=3881.5385$. 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 ${{x}^{2}}=\dfrac{555060}{165}=3364$ and hence, we get $x=58\text{ cm}$. This seems like the best option.
We can eliminate option (c) and (d) as well because dividing the area of the floor by the numbers given in these options will give us decimal values.
Hence, the number of square tiles having side length 58 cm to cover the floor is 165.

So, the correct answer is “Option (b)”.

Note: In this question, we faced insufficiency in the given information. But because it was a multiple choice question, we could use the given options to figure out the missing information and find the correct answer. In this type of questions, it is important that we understand which formulae and ratios are to be taken to obtain the desired answer.