I started by listing all the possible values of the sides with regard to the Triangle Inequality. To me, there are only 2 possible triangles: 222 and 231. Finding the area of 222 is easy, but how would I find the area of 231?
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A triangle cannot have side lengths $1,2,3$ units, as $3=2+1$, contradicting the triangle inequality (which is strict inequality). – Sarvesh Ravichandran Iyer Mar 26 '17 at 23:58
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2Note: The problem doesn't seem to specify that the sides are integers, so there are infinitely many possible triangles – lulu Mar 27 '17 at 00:03