Question

9.
of times.
A rectangular courtyard of length 20 m 16 cm and breadth 15 m 60 cm is to be
with same sized square tiles. Find the maximum possible number of such tiles.​

Answer 1

Solution :-

Given : A rectangular courtyard of length 20 m 16 cm and breadth 15 m 60 cm is to be with same sized square tiles.

Formula used :

Area of rectangle = (Length × Breadth) sq. units

Area of square = (side)² sq. units

Area of a rectangular courtyard = (2016 × 1560) cm²

= 3144960 cm²

For finding the maximum possible size of the square tiles we have to find its HCF :

By Prime factorisation :

2016 = 2^5 × 3 × 7

1560 = 2³ × 3 × 5 × 13

Each side of the square tile = HCF of 2016 and 1560 = 2³ × 3 = 24

Now, The maximum possible number of such tiles :

= Area of rectangular courtyard / Area of each square tile

= 3144960 cm² / (24 × 24) cm²

= 5460

Answer : The maximum possible number of such tiles = 5460