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Mathematics

A rectangular courtyard 3.78 m long and 5.25 m broad is to be paved exactly with square tiles, all of the same size. What is the largest size of such a tile? Also, find the number of tiles.

Mensuration

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Answer

Given,

Length = 3.78 m = 378 cm

Breadth = 5.25 m = 525 cm

The side of the largest square tile that can pave the floor exactly must be the HCF of the length and breadth of the courtyard.

HCF of 378 and 525 = 21 cm.

Number of tiles = Area of courtyardArea of each tile=378×52521×21\dfrac{\text{Area of courtyard}}{\text{Area of each tile}} = \dfrac{378 \times 525}{21 \times 21} = 450.

Hence, largest size of tile = 21 cm × 21 cm and total number of tiles = 450.

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