PRMO 2012 question 2

 2. A triangle with perimeter 7 has integer side lengths. What is the maximum possible area of such a triangle?

Possible side lengths:
1,1,5 => invalid (since sum of 2 sides should be more than the 3rd)
1,2,4 => invalid
1,3,3 => valid
2,2,3 => valid

So only 2 combinations are valid => 1,3,3 and 2,2,3.
Compute area by heron's formula for both the combinations.
The larger area is 3.sqrt(7)/4 and that's the answer.

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