You can put this solution on YOUR website! This is an interesting question. You can intuit the answer, or use more advanced math to get at it directly.
Given a length of one, I would measure out a side of length 2 and then a side of length 1 so that the two sides were perpendicular. Then, but the Pythagorean theorem, the hypotenuse has length sqrt(5). Thus, the perimeter is 1+2+sqrt(5)=3+sqrt(5).