Question

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

Answer 1

SOLUTION :  

GIVEN: Length of a rectangular yard = 18 m 72 cm  and breadth of a rectangular yard = 13 m 20 cm broad.

First , we need to find the HCF of the length and breadth of the rectangular yard to find the size of the square tile of same size needed to pave the rectangular yard.

Length of the  rectangular yard = 18 m 72 cm = 1800 cm + 72 cm = 1872 cm  

[1 m = 100 cm]

Breadth of the rectangular yard = 13 m 20 cm = 1300 cm + 20 cm = 1320 cm

[1 m = 100 cm]

The prime factors of 1872 and 1320 are :  

1872 = 2⁴ x 3² x 13

1320 = 2³ x 3 x 5 x 11

HCF of 1872 and 1320 = 2³ x 3

[HCF(Highest Common Factor) of two or more numbers= Product of the smallest Power of each common prime factor involved in the numbers.]

HCF of 1872 and 1320 = 24

Therefore, Length of side of the square tile = 24 cm

Number of tiles required = Area of the courtyard /  Area of each square tile

Number of tiles required = Length x Breadth / side²

Number of tiles required = (1872 cm x 1320 cm ) / 24 × 24 cm

Number of tiles required = 78 × 55 = 4290  

Number of tiles required = 4290.

Hence, the least possible number of tiles required is 4290.

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Answer 2

Solutions :-

Given :
A rectangular courtyard is 18m 72cm (1872 cm) long and 13m 20 cm (1320 cm) broad.


Find the area of rectangular courtyard :-

Area of rectangle = Length × Breadth square unit
= (1872 × 1320) cm²
= 2471040 cm²


Find the HCF of 1872 and 1320.

HCF of 1872 and 1320 is 24



Find the least possible number of such tiles :-

= Area of rectangular courtyard / Area of square tiles
= 2471040/24²
= 2471040/576
= 4290


Hence,
The least possible number of such tiles = 4290