Question

A mason has to fit a bathroom with square marble tiles of the largest possible size. The size of the bathroom is 10 ft by 8 ft. What should be the size in inches of the tile required that has to be cut and how many such tiles are required?

Answer 1

- Hint: In order to solve this question, we should know about the concept of HCF, that is, the highest common factor of the given number and the area of rectangle is calculated as, length $\times$ breadth and the area of square is calculated as, side $\times$ side. By using these concepts, we can find the answer to this question.

Complete step-by-step solution -
In this question, we have been asked to find the size of the square tile in inches and the number of square tiles which the mason would require to cover a bathroom of the size, 10 ft by 2 ft. To solve this question, we need to know that whenever we have to divide 2 or more natural numbers in small equal parts, we take their HCF. So, here to find the size of the square tile, we will take the HCF of 10 ft and 8 ft. So, we get,
$10=2\times 5$ and $8=2\times 2\times 2$
 Here, we can see that the highest common factor is 2. Hence, we can say that the sides of the square tile is 2 ft. Now, we know that 1 ft = 12 inches. So, we can say that 2 ft = $2\times 12=24$ inches. Therefore, we can say that the side of the square tile is 24 inches.
Now, to calculate the number of tiles required to cover the floor, we will use the formula,
Number of tiles to cover the floor = ${\displaystyle \frac{\text{Area of floor}\left(\text{in sq ft}\right)}{\text{Area of 1tile}\left(\text{in sq ft}\right)}}$
Now, we know that the area of rectangular floor = length $\times$ breadth and the area of square tile = side $\times$ side. So, we can write, area of floor = $10\times 8$ and area of tile = $2\times 2$. Therefore, we get,
Number of tiles to cover the floor = ${\displaystyle \frac{10\times 8}{2\times 2}}$
Number of tiles to cover the floor = $5\times 4=20$ tiles
Hence, we can say that the mason will require 20 square tiles of side 24 inches to cover the floor of the bathroom of size 10 ft by 8 ft.

Note: While solving this question, we need to remember that 1 ft =12 inches and while calculating the number of tiles by the formula, $\text{Number of tiles =}{\displaystyle \frac{\text{Area of floor}}{\text{Area of 1tile}}}$, both the areas should be of the same unit, either in sq. ft or in sq. inches, because this could be a possible mistake that one can make.