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The lengths of the sides of a right-angled triangle form a geometric sequence.

Find the two possible values for the common ratio of the sides.


Use Pythagoras' Theorem


Let the three sides be a,ar,ar2.

The two cases to consider are when

  • r>1 (so the sequence is increasing) and ar2 is the hypotenuse (as it is the longest side)

  • 0<r<1 and a is the hypotenuse.