# Sunday Times Teaser 2617 – A Case of Ambiguity

*by Des MacHale*

#### Published: 18 November 2012 (link)

Every schoolchild knows that it is possible for two triangles to have two of their lengths-of-sides in common and one of their angles in common without the two triangles being identical or “congruent”. This can happen when the common angle is not included between the two common sides. I have found such a pair of non-congruent triangles with all the lengths of the sides being a whole number of centimetres and with the longest side of each triangle being 10cm in length.

What are the lengths of the other two sides of the smaller triangle?

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Here is my solution:

Here is another version