Question

A rectangular courtyard of 10m44cm breadth and 15m12cm length is to be paved with same size square stones.Find the least possible number of such stones

Answer 1

1512-1044= 468; 1044-468=596;-596-468=128;468-128=340;340-128=212; 212-128 = 84; 128-84 =44; 84-44 =40; 44 - 40 =4. square titles 4 cm * 4 cm. 394632 tiles

Answer 2

Convert all units to cm:

10 m 44 cm = 1044 cm

15 m 12 cm = 1512 cm

Find the prime factors:

1044 = 2² x 3² x 29

1512 = 2³ x 3³ x 7

Find the HCF:

HCF = 2² x 3² = 36 cm

⇒ The biggest possible size of the stone to be used is 36 cm by 36 cm

Find the number of tiles length-wise:

Number of tiles = 1044 ÷ 36 = 29

Find the number of tiles breadth-wise:

Number of tiles = 1512 ÷ 36 = 42

Find the total number of tiles needed:

Number of tiles = 29 x 42 = 1218

Answer: The least number of square tiles needed is 1218