Size of Bathroom = 10 feet by 8
We know that 1feet = 12 inches
So, 10 feet = 10 X 12 => 120 inches
8 feet = 8 X 12 => 96 inches
Now, We will find the HCF of ( 120,96 ) to find the side of a square tile
By prime factorization method :-
120= 2^3 X 3 X 5
96 = 25 X 3
So, HCF ( 120 , 96 ) = 2^3 X 3 = 24 inch
Now, We will find the number of square tiles:-
Number of Square tiles = Area of Bathroom / Area of Square Tiles
= Length X Breadth / side^2
= 120 X 96 / 24 X 24
= 11520 / 576
= 20 tiles ANS
Alternate solution
find GCD of 10 and 8
It is 2.
1ft=12in, so 2ft=24in.
24 is the size (in inches),
To see how many are required,
8ft/24in
=8ft/2ft
=4
10ft/24in
10ft/2ft
=5
4×5=20
ANS: 20tiles of 24in side length.