1. Triangle Optimization

Hello:

I am presented with a problem in which I must maximize the area of a triangle with a perimeter of 12.

I do not necessarily want an answer with the numbers I provided, but rather the general step by step methodology in terms of how this problem is done.
Thanks so much, I am a bit lost as to how to optimize in the first place!

2. The area of triangle is
$\displaystyle S^2=s(s-x)(s-y)(s-z)$
$\displaystyle 12=x+y+z$
$\displaystyle s=12/2=6$
or
$\displaystyle S^2=6(6-x)(6-y)(6-z)=6(y+z-6)(6-y)(6-z)$
find max S with y and z.

3. Thanks! I really appreciate the help.. One last, quick thing.
The problem in question asks us to find the maximum area of a V shaped object with a perimeter of 12. The top of the V however, is not factored into the total perimeter (meaning each side of the V shape is 6 in length)
Does this change the calculation in any particular way? Should I "make up" an additional length for the open side in question and then subtract it out of my optimization equation in the end?