Question

A rectangular courtyard 378 cm long and 525 cm broad is to be paved exactly with square tiles, all of the same size. The minimum number of such tiles is :

Answer 1

Given length of rectangular courtyard

$=378cm$

breadth $=525cm$

Find the largest square tile :

largest square tile $=H.C.F(378,525)$

$378=2\times 3\times 3\times 21$

$525=5\times 5\times 21$

$H.C.F=21$

the length of largest square tile that can be paved exactly with other square tiles $=21cm$

Find the area of largest square tile :

Area = area of square $=side\times side$

Area $=21\times 21=441c{m}^2$

Find the area of courtyard :

Area of rectangular courtyard

$=length\times breadth$

$378\times 525=198450c{m}^2$

required minimum number of square tiles

$=198450/441=450tiles.$

therefore, minimum number square tiles

$=450$

we get

$450tiles$