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.

Answer 1

Given, 

Length of courtyard = 18 m 72 cm 

= 1800 cm + 72 cm 

= 1872 cm (∵1 m = 100 cm) 

Breadth of courtyard = 13 in 20 cm 

= 1300 cm + 20 cm 

= 1320 cm 

The size of the square tile needed to be paved on the rectangular yard is equal to the HCF of the length and breadth of the rectangular courtyard. 

Now, finding the prime factors of 1872 and 1320, we have 

1872 = 2⁴ × 3² × 13 

1320 = 2³ × 3 × 5 × 11 

⇒ HCF (1872 and 1320) = 2³ × 3 = 24 

∴ The length of side of the square tile should be 24 cm. 

Thus, the number of tiles required = (area of the courtyard) / (area of a square tile) 

We know that, area of the courtyard = Length × Breadth 

= 1872 cm × 1320 cm 

And, area of a square tile = (side)² = (24cm)² 

⇒ the number of tiles required = \(\frac{(1872 \times 1320)}{(24)^2}\) = 4290 

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