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Can you explain the strategy for winning this game with any target?

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2001 Spatial Oddity

Age 11 to 14
Challenge Level

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

A 16 cm by 9 cm piece of card can be cut into two pieces which can be rearranged to form a 12 cm by 12 cm square. 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.