Yes, there are non-square rectangles that admit a perfect squaring. The smallest number of squares in a perfect squaring of a rectangle is 9. All perfect squarings of rectangles using between 9 and 17 squares have been found and are listed here.

The unofficial logo of the Department of Combinatorics and Optimization at the University of Waterloo is actually a perfect squaring of the 32 $\times$ 33 rectangle using 9 squares.

Yes, there are non-square rectangles that admit a perfect squaring. The smallest number of squares in a perfect squaring of a rectangle is 9. On the other hand the smallest number of squares in a perfect squaring of a square is 21.

All perfect squarings of rectangles using between 9 and 17 squares have been found and are listed here. There appear to be many more rectangles that admit a perfect squaring than squares that admit a perfect squaring. See the quote by David Gale here.

The unofficial logo of the Department of Combinatorics and Optimization at the University of Waterloo is actually a perfect squaring of the 32 $\times$ 33 rectangle using 9 squares.

Yes, there are non-square rectangles that admit a perfect squaring. The smallest number of squares in a perfect squaring of a rectangle is 9. All perfect squarings of rectangles using between 9 and 17 squares have been found and are listed here.

Yes, there are non-square rectangles that admit a perfect squaring. The smallest number of squares in a perfect squaring of a rectangle is 9. All perfect squarings of rectangles using between 9 and 17 squares have been found and are listed here.

The unofficial logo of the Department of Combinatorics and Optimization at the University of Waterloo is actually a perfect squaring of the 32 $\times$ 33 rectangle using 9 squares.