Least Number of Square Tiles Required to Pave a Rectangular Courtyard

Video Explanation

Watch the video below to understand the complete solution step by step:

Solution

Question: A rectangular courtyard is 18 m 72 cm long and 13 m 20 cm broad. It is to be paved with square tiles of the same size. Find the least possible number of such tiles.

Step 1: Convert All Dimensions into Centimetres

Length = 18 m 72 cm = (18 × 100) + 72 = 1872 cm

Breadth = 13 m 20 cm = (13 × 100) + 20 = 1320 cm

Step 2: Find the Side of the Largest Square Tile

The side of the largest square tile is the HCF of 1872 and 1320.

Using Euclid’s division algorithm:

1872 = 1320 × 1 + 552

1320 = 552 × 2 + 216

552 = 216 × 2 + 120

216 = 120 × 1 + 96

120 = 96 × 1 + 24

96 = 24 × 4 + 0

∴ HCF (1872, 1320) = 24 cm

Step 3: Find the Number of Tiles Required

Number of tiles along the length = 1872 ÷ 24 = 78

Number of tiles along the breadth = 1320 ÷ 24 = 55

Total number of tiles = 78 × 55 = 4290

Final Answer

∴ The least possible number of square tiles required is 4290.

Conclusion

Thus, by using the HCF of the length and breadth of the courtyard, we find that the minimum number of square tiles needed is 4290.