A grid has lines at 90-degree angles. There are 12 lines in one direction and 9 lines in the other direction. Lines that are parallel are 11 inches apart. What is the least number of 12-inch by 12-inch floor tiles needed to cover all of the line intersect
To calculate the number of 12-inch by 12-inch floor tiles needed to cover all of the line intersections on the grid, we need to find the total area of the grid and divide it by the area of each tile.
First, let's calculate the total number of line intersections on the grid. Since there are 12 lines in one direction and 9 lines in the other direction, the total number of line intersections would be the product of these two numbers: 12 x 9 = 108.
Now, let's calculate the total area of the grid. Since the lines that are parallel are 11 inches apart, we can consider the distance between any two adjacent intersections as the size of the tile. Thus, the grid can be divided into 11-inch squares.
Since there are 12 lines in one direction, there would be 12 - 1 = 11 squares in that direction.
Similarly, since there are 9 lines in the other direction, there would be 9 - 1 = 8 squares in that direction.
Therefore, the total number of squares in the grid would be 11 x 8 = 88.
To calculate the area of the grid, we multiply the total number of squares by the area of each square (11 inches x 11 inches).
So, the total area of the grid is 88 x (11 inches x 11 inches) = 88 x 121 square inches.
Now, let's calculate the number of tiles needed.
Since each tile has an area of 12 inches x 12 inches, the total number of tiles needed would be the total area of the grid divided by the area of each tile:
Total number of tiles = (88 x 121 square inches) / (12 inches x 12 inches)
Dividing the total area by the area of each tile:
Total number of tiles = 10848 square inches / 144 square inches
Simplifying:
Total number of tiles = 75
Therefore, the least number of 12-inch by 12-inch floor tiles needed to cover all of the line intersections on the grid is 75.
To determine the least number of 12-inch by 12-inch floor tiles needed to cover all of the line intersections, follow these steps:
1. Calculate the total number of line intersections. Since there are 12 lines in one direction and 9 lines in the other direction, the total number of intersections will be the product of these two numbers: 12 x 9 = 108.
2. Count the number of parallel lines. In this case, the lines that are parallel are 11 inches apart. To cover all of these lines, we'll need to count the number of spaces between the lines and add 1. In this case, the number of spaces between the parallel lines is 11 - 1 = 10.
3. Determine the number of tiles needed to cover the line intersections. Since each tile is 12 inches by 12 inches, the area covered by one tile is 12 x 12 = 144 square inches. To find the number of tiles needed, divide the total area (in square inches) by the area covered by one tile: 108 x 144 = 15,552.
Therefore, the least number of 12-inch by 12-inch floor tiles needed to cover all of the line intersections is 15,552 tiles.