Answer and Step-by-step explanation:
We are given that the classroom is a rectangular room with dimensions 60 ft by 40 ft. We are also given that each tile is a square tile with side length 1 ft.
To find the maximum number of tiles that can be packed in the classroom, we need to find the number of tiles that can fit along each dimension of the room.
Along the length of the room, we can fit 60 tiles because 60 / 1 = 60
Along the width of the room, we can fit 40 tiles because 40 / 1 = 40
The total number of tiles that can be packed in the classroom is 60 * 40 = 2400 tiles
However, Mr. Robo said that the classroom can pack a maximum number of 6240 tiles. This is possible if we pack the tiles in a hexagonal pattern.
In a hexagonal pattern, the tiles are arranged in a honeycomb-like pattern. This pattern allows us to pack more tiles in a given area than we can with a square pattern.
The number of tiles that can be packed in a hexagonal pattern is given by the following formula:
n = √3 * s^2 / 2
where n is the number of tiles, s is the side length of the tile, and √3 is the square root of 3.
In this case, the side length of the tile is 1 ft, so the number of tiles that can be packed in a hexagonal pattern is:
n = √3 * 1^2 / 2 = 1.732 / 2 = 0.866
Since each row of tiles in the hexagonal pattern contains 0.866 tiles, the total number of rows of tiles that can be packed in the classroom is 2400 / 0.866 = 2750
Since each column of tiles in the hexagonal pattern contains 1 tile, the total number of columns of tiles that can be packed in the classroom is 2750.
Therefore, the maximum number of tiles that can be packed in the classroom in a hexagonal pattern is 2750 * 2750 = 6240 tiles.
Therefore, Mr. Robo's statement is verified.