Question : A mason has to fit a bathroom with square marble tiles of largest size possible. The size of bathroom is 10 ft. by 8 ft. What would be the size in inches of the tile required that has to be cut and how many such tiles are required?
Doubt by Vanshika
Solution :
Dimensions of Bathroom
Length = 10 ft
= 10×12 [∵1 ft = 12 inch]
= 120 inch
Breadth = 8 ft
= 8×12
= 96 inch
We need to find the side of the square.
The side of the square should be largest number which will divide both 120 and 96 completely. And We know, it will be given by the HCF of 120 and 96.
120 = 2³×3×5
96 = 2⁵×3
HCF = 2³×3
= 8×3
= 24
Hence, the required side of the each square tile would be 24 inch.
Now,
No. of total tiles required = (Area of Bathroom)/(Area of each tile)
= (120×96)/(24²)
= (120×96)/(24×24)
= 20
Hence, total number of tiles required would be 20.