Hahaha! Is this for Educ 439?
Either way the answer is:
Perimeter F(x)= 6+(Sqrt((X^2)+16))+(Sqrt((X-6)^2)+16))
The goal of the function is finding the hypotenuse of the two triangles not being used by the triangle you created. The last side, the base, will always be 6. Obviously, X can only be between 0-6.
Maximum = F(0),F(6)= 17.211 (approx)
Minimum = F(3) = 16
Hope this helps!