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Fibonacci Puzzle

The inner rectangle is surrounded by 4 squares. Its length and width are shown. You can vary its dimensions by dragging B. Some questions to consider:
  • Given the dimensions of the rectangle, find the area of the blue square.
  • Given the areas of two of the squares, find the dimensions of the rectangle.
  • Given the areas of the blue square and the inner rectangle, find the dimensions of the rectangle.
  • The spiral consists of 4 quarter arcs. If the length of the part EF is 200 cm, what is the length of the part CDE? Furthermore, if the length of the part CD is 80 cm, what is the length of the part DE and BC?