A rectangular courtyard is 18m 72cm long and 13m 20 cm broad. It is to be paved with square tiles of the same size. Find the least possible number of such tiles.

Given: A rectangular courtyard is 18m 72cm long and 13m 20 cm broad.

To find: Here we have to find the least possible number of tiles of the same size that can be paved in the rectangular courtyard.

Solution:

We know that:

1 metre  $=$  100 centimetre.

Length of the courtyard  $=$  18 m 72 cm  $=$  1872 cm.

Breadth of the courtyard  $=$  13 m 20 cm  $=$  1320 cm.

We need to calculate HCF of 1872 and 1320 to find the size of a square tile. 

Writing the numbers as a product of their prime factors:

Prime factorisation of 1872:

• $2\ \times\ 2\ \times\ 2\ \times\ 2\ \times\ 3\ \times\ 3\ \times\ 13\ =\ 2^4\ \times\ 3^2\ \times\ 13^1$

Prime factorisation of 1320:

• $2\ \times\ 2\ \times\ 2\ \times\ 3\ \times\ 5\ \times\ 11\ =\ 2^3\ \times\ 3^1 \times\ 5^1\ \times\ 11^1$

Finding the product of all common prime factors:

• $2^3\ \times\ 3\ =\ 24$

HCF(1872, 1320): 24

So, the side length of the square tile should be 24 cm.

Now,

Number of tiles  $=\ \frac{Size\ of\ courtyard}{Size\ of\ a\ tile}$

Number of tiles  $=\ \frac{1872\ \times\ 1320}{24\ \times\ 24}$

Number of tiles  $=\ 78\ \times\ 55$

Number of tiles  $=$  4290

So, the number of tiles required is 4290.

Tutorialspoint

Simply Easy Learning

Updated on: 10-Oct-2022

452 Views

Kickstart Your Career

Get certified by completing the course

Get Started