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Detailed explanation of the seventeenth question of Tianjin mathematics senior high school entrance examination in 2009
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17. As shown in the figure, there is a square paper ABCD with a side length of 5, which should be cut into two small squares with a side length of A and B, so A2+B2 = 52.

① The values of a and b can be (hint: the answer is not unique) (write only one group);

(2) Please design a general cutting method, draw a cutting line in the picture and splice it into two small squares, and explain that this cutting method is universal:

Solution: ① Make A2+B2 = 52. Considering the special situation of right triangle, the values of a and b can be 3,4 (the answer is not unique);

(2) first cut a square with a side length of 4; Cut the remaining three squares with a side length of 1 and two rectangles with a length of 3 and a width of 1, and then splice them into squares with a side length of 3.