In how many different ways can 12 square tiles be arranged?
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First assumption: you want to use all 12 squares in each rectangle.
Let’s assume the squares are 1 inch on a side (could be foot, or yard, or whatever, but 1 UNIT).
Now, a rectangle has a length and a width. 12 squares an inch on a side have a total area of 12 square inches. So, your rectangle will also be 12 square inches.
To get that, you could have a rectangle of the following dimensions:
1 X 12
2 X 6
3 X 4
That’s it. Three possible rectangles, using all 12 squares per rectangle.
Now, if you DON’T have to use all 12 squares in the rectangle, then you could make 6 rectangles, using 2 squares each, so each rectangle would be 1 X 2.
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