Question

4. A rectangular court yard is 20 m 16 cm long and 15 m 60 cm broad. It is to be paved with square-shaped tiles of the same size. Find the number of tiles required to pave the court yard. ha​

Answer 1

Answer:

24 cm

Step-by-step explanation:

The dimensions of courtyard are

Length = 20m 16cm = 2016cm

Breadth = 15m 60cm = 1560cm

Least possible side of square stones used = HCF of 2016 and 1560

We know that the prime factorization of 2016 = 2 × 2 × 2 × 2 × 2 × 3 × 3 × 7

1560 = 2 × 2 × 2 × 3 × 5 × 13

So HCF of 2016 and 1560 = 2 × 2 × 2 × 3 = 24

Hence, the least possible side of square stones used is 24cm.

We know that

No. of square stones which is used to pave the rectangular courtyard = Area of courtyard/ Area of stone By substituting the values

No. of square stones which is used to pave the rectangular courtyard = (2016 × 1560)/ (24)2 = 5460 Therefore, the least possible number of such stones is 5460