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A rectangular Courtyard is 18m 72cm …

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A rectangular Courtyard is 18m 72cm long and 13m 20cm broad it is to be paved with square tiles of same size find the least possible number of such tiles

    • Posted by Simran Sethi 6 years, 5 months ago

    CBSE > Class 10 > Mathematics
    • 1 answers

    Sia ? 6 years, 1 month ago

    Length of the  courtyard = 18 m 72 cm = 1800 cm + 72 cm = 1872 cm (therefore, 1 m = 100 cm)
    Breadth of the courtyard = 13 in 20 cm = 1300 cm + 20 cm = 1320 cm
    To find the square tile of maximum side we take the HCF of 1872 and 1320
    Prime factorization of 1872 = 24 {tex}\times{/tex} 32 {tex}\times{/tex} 13
    Prime factorization of 1320 = 23 {tex}\times{/tex} 3 {tex}\times{/tex} 5 {tex}\times{/tex} 11
    HCF of 1872 and 1320 = 23 {tex}\times{/tex} 3 = 24
    Therefore, Length of side of the square tile = 24 cm
    Number of tiles required = Area of the courtyard / Area of each tile = (Length {tex}\times{/tex} Breadth) /Side2
    = (1872 cm {tex}\times{/tex} 1320 cm) ÷ (24 cm {tex}\times{/tex} 24 cm) = 4290.
    Hence 4290 tiles are required.

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