Pre rmo 2012
A triangle with perimeter 7 has integer side lengths.What is the maximum possible area of such a triangle?
The answer is of the form .Enter your answer as the sum of , and .
The answer is 14.
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SIMPLE! Since its perimeter is 7, and the lengths of sides are integers, imagine the number of triads whose sum equals 7. Since its a triangle, the sum of any two sides should be greater than the third side and their difference should be less than the third side.
THis leaves us with the triad ( 2,3,2) Using Heron's formula, s=3.5, Therefore, Area= 3(root 7)/4
a=3, b=7, c=4 a+b+c= 14
Thus, 14 is the answer!