Geom-ber Theory!
Consider a triangle of integer side lengths with integer perimeter. Can there exist a number of distinct possible integer triangles with the same perimeter that is exactly , where is strictly positive integer?
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1 solution
One triangle can be taken as ( 3 k 2 , 3 k 2 , 3 k 2 ) as side lengths and other triangle can be taken as ( 2 k 2 , 3 k 2 , 4 k 2 ) as side lengths.
This clearly satisfies the given condition.