There may be better, but I was at least able to get each number 1-15 using the number of (infinite) lines as I said originally...That's kind of neat, considering the square constructions had to be completely different than what I doing using line segments...but still got the same numbers...

This is actually a duplicate puzzle as the one I posted a long while ago on these forums:

The only difference is the perimeter would obviously be twice the "SUM" in the problem I posted...but just divide by 2, and it's the same logic to figure out...I love this puzzle...