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20 December

Permanent link to this puzzle: mscroggs.co.uk/puzzles/advent2016/20
Earlier this year, I wrote a blog post about different ways to prove Pythagoras' theorem. Today's puzzle uses Pythagoras' theorem.
Start with a line of length 2. Draw a line of length 17 perpendicular to it. Connect the ends to make a right-angled triangle. The length of the hypotenuse of this triangle will be a non-integer.
Draw a line of length 17 perpendicular to the hypotenuse and make another right-angled triangle. Again the new hypotenuse will have a non-integer length. Repeat this until you get a hypotenuse of integer length. What is the length of this hypotenuse?
If you enjoyed this puzzle, check out Sunday Afternoon Maths LIX,
puzzles about spheres, or a random puzzle.
© Matthew Scroggs 2017