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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.
A circle touches the lines OA, OB and AB where OA and OB are perpendicular. Show that the diameter of the circle is equal to the perimeter of the triangle
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A circular plate rolls in contact with the sides of a rectangular tray. How much of its circumference comes into contact with the sides of the tray when it rolls around one circuit?