The dimension of the room are 16 meters in length and 8 meters wide.A contracter wants to tile the room using the least number of square tiles.What should the tile dimension be?

Answer 1

To find the least number of square tiles needed to cover the room, we need to find the area of the room and the area of each tile, and then divide the two.

The area of the room is:

Length x Width = 16m x 8m = 128m²

Let x be the side length of each square tile.

The area of each tile is:

x²

To find the least number of tiles needed, we want to divide the area of the room by the area of each tile, and get a whole number:

128m² / x² = n, where n is a whole number

We can simplify this equation by multiplying both sides by x²:

128m² = n x²

To find the smallest value of x that makes n a whole number, we need to find the factors of 128 that are perfect squares. The factors of 128 are:

1, 2, 4, 8, 16, 32, 64, 128

The perfect squares among these factors are:

1, 4, 16, 64

We can try each of these values for x, and see which one gives a whole number for n:

For x = 1m, n = 128m² / 1m² = 128 (not a perfect square)
For x = 2m, n = 128m² / 4m² = 32 (a perfect square)
For x = 4m, n = 128m² / 16m² = 8 (a perfect square)
For x = 8m, n = 128m² / 64m² = 2 (not a perfect square)

So the tile dimension should be 4 meters by 4 metres, which gives us 32 square metres for each tile. This means we will need 128m² / 32m² = 4 tiles to cover the room.

Answer 2

GCF(8,16) = 8
so using 8x8 tiles, you will need only 1x2 = 2 tiles

Answer 3

I apologize for the mistake in my previous response. Yes, you're correct that the GCF of 8 and 16 is 8, and using 8x8 tiles would require only 2 tiles to cover the room. Thank you for pointing that out.