Rectangle Cutting

Tom and Jerry start with identical sheets of paper. Each one cuts his sheet in a different way. Can you find the perimeter of the original sheet?
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Problem



Tom and Jerry started with identical rectangular sheets of paper. Each of them cut his sheet in half. Tom obtained two rectangles, each with a perimeter of $40$cm while Jerry obtained two rectangles, each with a perimeter of $50$cm. What was the perimeter of Tom's original sheet of paper?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.