A rectangular courtyard is 18m72cm long and 13m20cm broad.It is to be paved with square tiles of same size.find the least possible number of such tiles.

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Solution

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 Euclid’s 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.

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