A square is a quadrilateral with four equal sides. The width of this rectangle is 12 cm and the length is 15 cm. Therefore, the maximum side length of a square can only be 12 cm, and cannot be longer than the shortest side of this rectangle, that is, the width. All four sides of a folded square should be 12 cm.

If you want to fold into a square, you can only take the minimum length of the rectangle, which is 12 cm. The width of this rectangle should be reduced by 3 cm. Because it is to be folded into a square, the length of each side should be consistent, so the maximum can only be 12 cm.

Extended data:

This involves the knowledge of primary school mathematics, the nature of squares, and the nature of rectangles. All four sides of a square are equal and all four corners are 90 degrees, which is a unique property of a square. The length and width of a rectangle can be unequal, but the opposite sides must be equal, which is a unique property of a rectangle.

From these properties, we can get the answer to this question. When a rectangle is folded into a square, the area will definitely decrease, because the four sides of the square must be equal and one side of the rectangle must be longer. When it becomes a square, part of it must be folded in. The side length here is 12 cm.