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
Length of the rectangular courtyard = 20m 16cm = 2,016cm
Breadth of the rectangular courtyard = 15m 60cm = 1,560cm
Least possible side of the square stones used to pave the rectangular courtyard = HCF of (2,016 and 1,560)
Prime factorization of 2,016 =2 × 2 × 2 × 2 × 2 × 3 × 3 × 7
Prime factorization of 1,560 = 2 × 2 × 2 × 3 × 5 × 13 HCF of (2,016, 1,560) = 2 × 2 × 2 × 3= 24
Least possible side of square stones used to pave the rectangular courtyard is 24 cm. Number of square stones used to pave the rectangular courtyard
= Area of rectangular courtyard Area of square stone = 2016cm × 1560cm (24cm) 2 = 5460 Thus, the least number of square stones used to pave the rectangular courtyard is 5,460.
Breadth of the rectangular courtyard = 15m 60cm = 1,560cm
Least possible side of the square stones used to pave the rectangular courtyard = HCF of (2,016 and 1,560)
Prime factorization of 2,016 =2 × 2 × 2 × 2 × 2 × 3 × 3 × 7
Prime factorization of 1,560 = 2 × 2 × 2 × 3 × 5 × 13 HCF of (2,016, 1,560) = 2 × 2 × 2 × 3= 24
Least possible side of square stones used to pave the rectangular courtyard is 24 cm. Number of square stones used to pave the rectangular courtyard
= Area of rectangular courtyard Area of square stone = 2016cm × 1560cm (24cm) 2 = 5460 Thus, the least number of square stones used to pave the rectangular courtyard is 5,460.
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