A rectangular courtyard is 18m72cm long and 13m20cm broad. It is to be paved with square tiles of the same size. Find the least possible no.of such tiles??
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
