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Is There a Theorem?

Draw a square. A second square of the same size slides around the first always maintaining contact and keeping the same orientation. How far does the dot travel?

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2001 Spatial Oddity

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

16cm x 9cm sqaure, cut, then made into 12cm x 12cm square.

With one cut a piece of card 16 cm by 9 cm can be made into two pieces which can be rearranged to form a square 12 cm by 12 cm. Explain how this can be done.

Find the dimensions of other rectangles that can be cut into exactly two pieces and rearranged to form a square.