a tile floor pattern is made of 36 square tiles, the tiles form a rectangle, the length of the long side of the rectangle is 42.75 inches.
which is the side length, in inches of 1 tile?
1.25
4.25
4.75
10.75
To find the side length of one tile, we need to establish a relationship between the total number of tiles, the shape they form, and the given dimensions of the rectangle.
Given that the tiles form a rectangle and there are 36 tiles, this implies that the rectangle's length and width—in terms of the number of tiles—must be two factors of 36. The factors of 36 that are possible dimensions for the rectangle (since the length is longer than the width) could be as follows:
1 x 36
2 x 18
3 x 12
4 x 9
6 x 6
Out of these, the 6 x 6 configuration would create a square, not a rectangle, so we can discard this possibility since it's stated they form a rectangle.
Now, we know the length of the longer side of the rectangle is 42.75 inches. Let's find a side length that will multiply by a whole number to give 42.75 inches. We can try each of the provided options to see if they work with the configuration of the tiles and the given length of 42.75 inches.
1.25 inches: This would not account for the full 42.75 inches with a whole number of tiles since 42.75 / 1.25 = 34.2, which is not a whole number and doesn't match with the configurations we have.
4.25 inches: This might be possible since we can have a whole number when we divide 42.75 by 4.25. Let's test it:
42.75 / 4.25 = 10. This means that if one side of the tile is 4.25 inches, there would be 10 tiles along the length of the rectangle.
Since there are 36 tiles in total, the width would need to have 36 / 10 = 3.6 tiles, which is not possible since we cannot have a fractional number of tiles.
4.75 inches: Let's check if this length gives us whole numbers:
42.75 / 4.75 = 9. This means that if one side of the tile is 4.75 inches, there would be 9 tiles along the length of the rectangle.
Since there are 36 tiles in total, the width would need to have 36 / 9 = 4 tiles, giving us a 4 x 9 configuration for the rectangle, which makes sense and works perfectly.
10.75 inches: This would exceed the count of the number of tiles along the long side because 42.75 / 10.75 = 4, which would suggest a 4-tile-long rectangle, but multiplying this by 9 (to make up 36) does not work because the width cannot be 9 times larger than the length in the given configuration.
Therefore, from the options provided, the side length of one tile that adds up to the correct length of 42.75 inches and corresponds to a rectangle configuration with 36 tiles is 4.75 inches.