Three identical rectangular cards can be placed end to end (with their short sides touching) to make rectangle A, and can be placed side by side (with their long sides touching) to make rectangle B. The perimeter of rectangle A is twice the perimeter of rectangle B. Find the ratio of the length of a short side to the length of a long side of each card (giving your ratio in its simplest form).
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Junior Mathematical Olympiad 2004 (2004)
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