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Equal lengths

The picture below shows two copies of the same rectangle with red and blue lines. The blue line visits the midpoint of the opposite side. The lengths shown in red and blue are of equal length.
What is the ratio of the sides of the rectangle?

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If you enjoyed this puzzle, check out Sunday Afternoon Maths LXIV,
puzzles about rectangles, or a random puzzle.
© Matthew Scroggs 2019