Question

exactly
5. A rectangular courtyard is 20 m 16 cm long and 15 m 60 cm broad. It is to be paved with
square stones of the same size. Find the least possible number of such stones.
6. Determine the longest tape which can be used to measure exactly the lengths 7 m, 3 m 85 cm
and 12 m 95 cm.​

Answer 1

solution:Length of the rectangular courtyard = 20 m 16 cm = 2,016 cm

Breadth of the rectangular courtyard = 15 m 60 cm = 1,560 cm

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 = 2016 cm × 1560 cm (24 cm) 2 = 5460 Thus, the least number of square stones used to pave the rectangular courtyard is 5,460.

*therefore this is the appropriate answer