Optimal Triangles

What is the largest possible area that can be found in a triangle with perimeter 12? We will call this shape an optimal triangle for this exploration.
What are some properties of the optimal triangles? What is another name for this triangle?

Try this exploration again, but try a different perimeter. Is the optimal triangle the same or different? Do you think the results of the exploration will be the same, regardless of the perimeter used? Explain why or why not.