Question

Manoj has to lay tiles on the floor. The size of the room is 9 feet × 12 feet. In the market, there are three kinds of square tiles 1 foot × 1 foot, 2 feet × 2 feet and 3 feet × 3 feet. Which size of tile should he buy for his room, so that he can lay it without cutting?

Answer 1

Size of the room = 9 feet ×12 feet
Factors of 9 = 1,3,9
Factors of 12 = 1,2,3,4,6,12

He can use the tile without cutting if the size of the sides of the tile is the common factor of 9 and 12.

Now, we will check different tile sizes, 1 foot × 1 foot
As 1 is the common factor of both 9 and 12 it can be used without cutting.

2 feet × 2 feet
As 2 is not the common factor of 9 and 12, it cannot be used.

Similarly, 3 is the common factor of both 9 and 12.
Hence, it can also be used.

Both 1 foot × 1 foot and 3 feet × 3 feet can be used for tiling.