Question

Suppose you’re tiling the floor of a 10 ft by 10 ft room, and find that 100 tiles will be needed.How many tiles will be needed to tile the floor of a 50 ft by 50 ft room?

Answer 1

We know that we need 100 tiles for a 10 ft by 10 ft room.

We have to calculate how much we will need for a 50 ft by 50 ft room.

We have at least ways to find this values.

One of the ways is to find the area covered per tile, and then calculate the number of tiles needed for a 50 x 50 ft room.

The other is taking into account the scale of the sides: when we increase the side length from 10 ft to 50 ft, the scale factor for each dimension is 5.

Then, the area will increase by a factor of 5² = 25.

Then, we will need 25 times the tiles we used for a 10 x 10 ft room.

Then, the number of tiles needed is:

`n=25*100=2500\text{ tiles}`

We can use the first method to check the answer.

The 10x10 ft room has an area of 10*10 = 100 ft². If we need 100 tiles for this floor, each tile covers one square foot.

We can now calculate the area of the 50x50 ft floor:

`A=50*50=2500\text{ sq. ft.}`

Then, if each tile covers one square foot, we will need 2500 tiles.

Answer: 2500 tiles.