Question

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

Answer 1

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

18m72cm = 1872cm and 13m20cm = 1320cm

now ,
let us find the hcf of 1872 cm and 1320 cm

=>[we can use  Euclids division lemma method]

=>hcf will be 24

now ,

=>Number of tiles required = (Area of rectangular courtyard)/(Area of square tile)

= (1872 × 1320)/(24 × 24)

= 4290 [sq.cm tiles]

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hope it helps u.......

Answer 2

The edges of rectangular courtyard are 1872 cm (18 m 72 cm) and 1320 cm (13 m + 20 cm).

On taking out HCF of 1872 and 1320 using Euclid's Lemma, we get

⇒ 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 we get HCF 24 cm with is edge of each square tile.

No. of tiles required = Area of courtyard / Area of tiles

No. of tiles required = (1872 × 1320)/(24 × 24) = 4290

Answer : 4290 tiles