Question

The minimum number of square-shaped tiles required to exactly cover a room of length 160 cm and breadth 100 cm is:

[1 mark]

• A. 80
• B. 40
• C. 20
• D. 10

Answer 1

The correct option is B 40

$Numberoftilesrequired=\frac{Areaofroom}{Areaoftile}$

Length of tile = HCF of length and breadth of the room

Prime factorisation of $160=2^5\times 5^1$

Prime factorisation of $100=2^2\times 5^2$

HCF of 160, 100 = 20

Length of tile = 20 cm

Area of tile ${20}^2=400c{m}^2$

$Areaoftheroom=160\times 100=16000c{m}^2$

$\therefore Theminimumnumberoftilesrequired=\frac{16000}{400}=40$