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I drew four right-angled triangles. The hypotenuse of my first triangle was also the shortest side of my second triangle; the hypotenuse of my second triangle was also the shortest side of my third triangle; the hypotenuse of my third triangle was also the shortest side of my fourth triangle. The length in millimetres of each side of each triangle was an integer less than 100.

How do you solve this?

*What were the lengths of the shortest and the longest sides that I drew?

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    $\begingroup$ Was it really all 4 triangles with integer sides all less than 100, or just the first 3? $\endgroup$ – Geoff Robinson Mar 3 '15 at 9:55
  • $\begingroup$ I go along with @GeoffRobinson. I think we have a sequence 2,3,5,12,13,84,85, x with x larger than 100 $\endgroup$ – Dan Mar 3 '15 at 10:04
  • $\begingroup$ Definitely all 4. $\endgroup$ – user220640 Mar 3 '15 at 10:06
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    $\begingroup$ @GeoffRobinson, reinbot: I'll give you a hint - the shortest side of all is 9 mm, and the longest is 97 mm. $\endgroup$ – TonyK Mar 3 '15 at 10:08
  • $\begingroup$ @TonyK: okay, now I got it ;-) $\endgroup$ – Dan Mar 3 '15 at 10:12

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