Question

A rectangular courtyard is 20m 16cm long and 15m 60cm broad. It is to be paved with square stones of the same size. Find the least possible number of such stones.

Answer 1

The dimensions of courtyard are

Length = 20 m 16 cm = 2016 cm

Breadth = 15 m 60 cm = 1560 cm

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

We know that the prime factorization of

$2016=2\times 2\times 2\times 2\times 2\times 3\times 3\times 7$

$1560=2\times 2\times 2\times 3\times 5\times 13$

So HCF of 2016 and $1560=2\times 2\times 2\times 3=24$

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

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 $=\frac{(2016\times 1560)}{(24{)}^2}$

$=84\times 65$

= 5460

Therefore, the least possible number of such stones is 5460.