If there are 12 square tiles and each tile measure 1 foot on each side ,how many non congruent rectangle can you make.Each rectangle must use all 12 tiles
1 by 12
2 by 6
3 by 4
Thanks
To find the number of non-congruent rectangles that can be made using the 12 square tiles, we can approach it by considering the possible dimensions of the rectangles.
First, let's list down the factors of 12: 1, 2, 3, 4, 6, and 12. These represent the possible lengths and widths of the rectangle.
Now, let's consider each factor and determine if a rectangle can be formed using all 12 tiles.
1. For a length of 1, the width would be 12 (1 x 12). However, since the length and width of the rectangle must be non-congruent, this option is not valid.
2. For a length of 2, the width would be 6 (2 x 6). This forms a valid rectangle.
3. For a length of 3, the width would be 4 (3 x 4). Again, this forms a valid rectangle.
4. For a length of 4, the width would be 3 (4 x 3). This forms a valid rectangle.
5. For a length of 6, the width would be 2 (6 x 2). Once again, this forms a valid rectangle.
6. For a length of 12, the width would be 1 (12 x 1). However, since the length and width of the rectangle must be non-congruent, this option is not valid.
Therefore, there are a total of four non-congruent rectangles that can be made using the 12 square tiles.