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

Given: Size of the bathroom is 10 ft. by 8 ft.

To find: Size in inches of the tile required that has to be cut and the number of tiles required.

Solution:

We need to find the size of tiles in inches. So let's convert the size of the room in inches.

We know that:

1 ft. $=$ 12 inches

Now,

Size of the room  $=\ (10\ \times\ 12)$ inches by $(8\ \times\ 12)$ inches

Size of the room  $=\ 120$ inches by $96$ inches

So, the largest size of tile required will be the HCF of 120 and 96.

Using Euclid's division algorithm to find HCF:

Using Euclid’s lemma to get: 

• $120\ =\ 96\ \times\ 1\ +\ 24$

Now, consider the divisor 96 and the remainder 24, and apply the division lemma to get:

• $96\ =\ 24\ \times\ 4\ +\ 0$

The remainder has become zero, and we cannot proceed any further. 

Therefore the HCF of 120 and 96 is the divisor at this stage, i.e., 24.

So,

Size of the tile in inches $=$ 24 inches by 24 inches

Now,

Number of tiles required  $=\ \frac{Area\ of\ the\ bathroom}{Area\ of\ a\ tile}$

Number of tiles required  $=\ \frac{120\ \times\ 96}{24\ \times\ 24}$

Number of tiles required  $=\ 5\ \times\ 4$

Number of tiles required  $=$  20

So, 20 number of tiles are required of size 24 inches by 24 inches.

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Updated on: 10-Oct-2022

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