SOLUTION: How many distinct triangles have a perimeter of 15 units and integral length sides?

Question 200809: How many distinct triangles have a perimeter of 15 units and integral length sides?
Answer by vleith(2983) (Show Source): You can put this solution on YOUR website!
I'm sure there must be an algebraic way to do this, but for this one, I would just grind through them.
Start with an equilateral triangle 5,5,5
Now take one unit from one side and add it another side, 4,6,5 or 4.5,6. which leaves unique one of 4,6,5
Again 3,7,5 or 3,6,6
Again 2,8,5 or 2,7,6 or 2,7,6 or 2,7,6 which leaves just 2,8,5 and 2,7,6
Again 1,9,5 or 1,8,6 or 1,7,7
So we have 7 possibilites. Look at the possible answers and make sure that for each, the sum of any two sides is greater than the remaining side.
1,9,5 won't work since 1+5 <9
Likewise 2,8,5 wont work since 2+5<8
So I say we have 5 that work
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