Is it possible to obtain a 12×12 carpet by cutting a 16×9 carpet once?

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Yesterday my brother asked me a question.

Suppose you have a carpet of size $16×9$. Now you have to cut this carpet in such a way that after cutting it and arranging pieces, the dimension is $12×12$. You can only cut the carpet once. You can arrange the obtained pieces in any way you like. How can you do this?

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enter image description here Essentially the same problem appears in Boris Kordemsky's puzzle book, with the solution as below. enter image description here