Question

Manoj has made a new house. He wants 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.
And there are 3 kinds of square tiles, 1 foot × 1 foot, 2 feet × 2 feet and 3 feet × 3 feet.
Now, size of tile that he should choose to lay it without cutting should be a factor of 9 and 12 both.
As we know, 1 is a factor of all the numbers, so he can buy tiles of measure 1 foot × 1 foot.
Now, 2 is not a factor of 9, so tiles of measure 2 foot × 2 foot cannot be laid without cutting.
Also, we know 3 is a factor of 9 and 12 both, so he can also choose the tiles of measure
3 feet × 3 feet.
Thus, he can buy tiles with measure 1 foot × 1 foot or 3 feet × 3 feet for his room.