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13 November, 13:43

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?

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  1. 13 November, 13:48
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    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
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