A rectangular courtyard is $18 m 72 cm$ long and $13 m 20 cm$ long and broad. It’s to be paved with square tiles of the same size, then the smallest possible number of such tiles is ____.

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Detailed Solution

A rectangular courtyard is

18 m 72 cm

long and

13 m 20 cm

broad. It’s to be paved with square tiles of the same size, then the smallest possible number of such tiles is 4920.
From the given data, the length and breadth of a rectangular courtyard are

18 m 72 cm

and

13 m 20 cm

respectively.
We know that 1m = 100 cm.

⇒ 18 m 72cm = 18 × 100 + 72 = 1800 + 72 = 1872 cm 13 m 20cm = 13 × 100 + 20 = 1300 + 20 =1320cm

The edge of the square tile must be the common factor of the scale of the courtyard.
So, the full fringe of square tile = HCF of 1872 and 1320.

1872 = 2 × 2 × 2 × 2 × 3 × 3 × 13 1320 = 2 × 2 × 2 × 3 × 5 × 11 ⇒ H C F = 2 × 2 × 2 × 3 = 24 cm

Thus, the full fringe of the square tile = 24cm.
So, the required number of tiles is,

= Area of courtyard Area of square tiles = 1872 × 1320 242

= 1872 × 1320 24 × 24 = 4290

Thus, the smallest possible number of tiles required to hide the courtyard is 4290.

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