Question

a 5.25m by 3.78m rectangular courtyard iis to be paved with square tiles of the same size such that only whole tiles are used.what is the largest possible size of such a tile?also find the number of tiles required

Answer 1

Length of field = 5.25m = 525cm
Breadth of field = 3.78m = 378cm
Let side of one square tile be 'x' cm

Therefore,
=> No. of rows = length/x = 525/x
=> No. of columns = breadth/x = 378/x

These numbers must be whole numbers, meaning x has to be a factor of both 525 and 378.Therefore, the greatest value of x
= Highest Common Factor (HCF) of 525 and 378
= 21
Therefore, largest possible tile size is 21m

Area of one tile = (21)^2 = 441sq.m
Area of field = 525*378 = 198450sq.cm
Therefore, no. of tiles required = 198450/441 = 450

Answer 2

Largest possible size of tile is 21 cm. And the number of tiles is 450.