Question

A $4m\times 6m$ floor is to be covered uniformly with identical square tiles. What should be the size of each tile, so that they fit the floor exactly?

• A. (4m x 4m)
• B. (3m x 3m)
• C. (2m x 2m)
• D. (6m x 6m)

Answer 1

The correct option is C (2m x 2m)

For the given floor, if we choose a square tile of $4m\times 4m$, it won't fit the length which is of 6 meters and we'll need to cut a tile.

If we take the tile of $3m\times 3m$ then it'll fit the length but for the width which is of 4 meters, we'll need to cut a tile.

Similarly, the tile of $6m\times 6m$ would fit for the length but not for the width.

Whereas if we take tiles of $2m\times 2m$, we wouldn't need to cut the tile as it would easily fit the floor.

Aliter - Here, the dimensions of the room were not that big so we could figure out which size of square tile would fit the floor. But if the dimensions are big then it would be difficult to do this way. So instead what we can do, we can find H.C.F of the dimensions of the room.

H.C.F of 4 & 6 = 2.

So, the size of the square tile that would fit the floor can be $2\times 2$.

An important thing to notice here is that we cannot choose any dimension which is higher than $2\times 2$ but we can choose a dimension lower than $2\times 2$ of which $2\times 2$ is a multiple. Like - $1\times 1$ or $0.5\times 0.5$.