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To determine how many rectangles of different sizes can be formed from 36 identical squares, we first need to find the possible dimensions of rectangles that can be created using these squares. The total area of the rectangles must equal 36, which can be expressed as ( length \times width = 36 ). The pairs of factors of 36 are (1, 36), (2, 18), (3, 12), (4, 9), and (6, 6), leading to 10 unique rectangles when considering both orientations (length × width and width × length). Thus, a total of 10 different rectangles can be formed.
144
The following rectangles have a length and width that make an area of 36: 1 x 36; 2 x 18; 3 x 12; 4 x 9; 6 x 6
3 squares: 36 + 4 + 1 2 squares: 25 + 16
There is an infinite number that can have that perimeter