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By definition, an isosceles triangle has 2 of the 3 sides with the same length. From this, we already know that the third side must be or 5 or 12.
We also know that, for every triangle, the sum of two sides must be always bigger than the third side, for any combination.
From this second affirmation, we know that the third side can not be 5, because:
From this, we conclude that the third side of an isosceles triangle with sides equal to 5 and 12 is equal to 12.
See the attached photos.
Wrote this out pretty messy, sorry!
