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

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

Solution:

GIVEN: A rectangular yard is 18 m 72 cm long and 13 m 20 cm broad .It is to be paved with square tiles of the same size.

TO FIND: Least possible number of such tiles.

Length of the yard = 18 m 72 cm = 1800 cm  + 72 cm = 1872 cm               (∵ 1 m = 100 cm)

Breadth of the yard =13 m 20 cm = 1300 cm + 20 cm = 1320 cm

The size of the square tile of same size needed to the pave the rectangular yard is equal the HCF of the length and breadth of the rectangular yard.

Prime factorisation of $1872=2^{4} \times 3^{2} \times 13$

Prime factorisation of $1320=2^{3} \times 3 \times 5 \times 11$

HCF of 1872 and $1320=2^{3} \times 3=24$

∴ Length of side of the square tile = 24 cm

Number of tiles required $=\frac{\text { Area of the courtyard }}{\text { Area of each tile }}=\frac{\text { Lenght } \times \text { Breadth }}{(\text { Side })^{2}}=\frac{1872 \mathrm{~cm} \times 1320 \mathrm{~cm}}{(24 \mathrm{~cm})^{2}}=4290$

Thus, the least possible number of tiles required is 4290.