You have 12 square tiles,each tile measures 1 foot on each side,how many non congruent rectangles can you make ?,each rectangle must use ll 12 tiles
To determine the number of non-congruent rectangles you can make with 12 square tiles, we need to consider the different ways we can arrange and combine the tiles.
One approach to solving this problem is to list out all the possible dimensions of the rectangles and check if they can be formed using the given tiles.
Since each tile measures 1 foot on each side, we can consider the dimensions of the rectangles in terms of the number of tiles they use for the length and width.
Let's start with the smallest rectangle that can be formed, which would be a 1x1 square. In this case, we would use a single tile.
Next, let's move on to rectangles that are 1 tile wide. We can have rectangles that are 1 tile by 2 tiles (1x2), 1x3, 1x4, and so on until 1x12. Since we have 12 tiles, any rectangle that is 1 tile wide and uses less than or equal to 12 tiles can be formed.
Similarly, let's consider rectangles that are 2 tiles wide. We can have rectangles that are 2x2, 2x3, 2x4, ..., 2x6.
Continuing this pattern, we can consider rectangles that are 3 tiles wide, 4 tiles wide, and so on until 6 tiles wide.
To summarize, the possible dimensions for the rectangles in terms of the number of tiles they use can be represented as follows:
1x1, 1x2, 1x3, 1x4, 1x5, 1x6, 1x7, 1x8, 1x9, 1x10, 1x11, 1x12
2x2, 2x3, 2x4, 2x5, 2x6
3x3, 3x4, 3x5, 3x6
4x4, 4x5, 4x6
5x5, 5x6
6x6
By counting the total number of different dimensions, we can determine the number of non-congruent rectangles that can be formed using the given tiles. In this case, there are 27 such rectangles.
Now that you know the possible dimensions, you can verify them by using the tiles physically or draw them on a piece of paper to confirm that they can indeed be formed using the given tiles.