Would this make a good high school math problem?

I was reading a book that said that not many opportunities are provided in high school math to strategize the solution of a problem. It gave the following problem as an example but did not elaborate. After thinking about it, I would have to agree. I am not interested in the solution so much as in finding strategies to narrow the number of cases to investigate.

How many different triangles are there with whole number length sides whose perimeter is 13? Keep in mind that the sum of the lengths of any two sides must be greater than the length of the third side.