Question

Square tiles of equal dimensions are to be laid in a lavish bathroom of size 90-inch $\times$ 126- inch. What should be the maximum dimension of a tile so that it covers the floor perfectly? How many such tiles are required?

• A. Dimension of tiles= 16 inch, No. of tiles = 6
• B. Dimension of tiles = 18 inch, No. of tiles = 26
• C. Dimension of tiles = 18 inch, No. of tiles = 35
• D. Dimension of tiles = 25 inch, No. of tiles = 12

Answer 1

The correct option is C Dimension of tiles = 18 inch, No. of tiles = 35

The dimension of the tile should be the smallest number which divides both the length and breadth of the bathroom so that it fits completely across its length as well as breadth.
Thus, we should calculate the HCF of 90 and 126.
$90=2\times 3^2\times 5$
$126=2\times 3^2\times 7$
$HCF=2\times 3^2=18$
Thus, the dimension of the square should be $18inch\times 18inch$.
For finding the number of tiles required, we need to calculate the total area of the bathroom and divide it by the area of one tile.
Therefore, number of tiles required= $\frac{90\times 126}{18\times 18}=35$