Question

12. A rectangular courtyard is 18 m 72 cm long and 13 mand 20 cm broad.
It is to be paved with square tiles of the same size. Find the least possible
number of such tiles.​

Answer 1

Given length of rectangular courtyard = 18 m 72 cm = 1872 cm Width of rectangular courtyard = 13 m 20 cm = 1320 cm To find the square tile of maximum side we take the HCG of 1872 and 1320 By Euclids division lemma we have 1872 = 1320 × 1 + 552 1320 = 552 × 2 + 216 552 = 216 × 2 + 120 216 = 120 × 1 + 96 120 = 96 × 1 + 24 96 = 24 × 4 + 0 Hence the HCF is 24 Therefore maximum side of the square = 24 cm Number of tiles required = (Area of rectangular courtyard)/(Area of square tile) = (1872 × 1320)/(24 × 24) = 4290 Hence 4290 tiles are required.