Remember your boundary:

So, you want to maximize area while minimizing perimeter. We can pretend that instead of a triangle, we are going to maximize the area for a rectangle (since this is easier) and divide our resultant area by two. So, let's maximize the area for the rectangle with sides where our perimeter must be where is a constant (we don't need to know what is). If we maximize that area, then we have also maximized the area of the triangle.

Area for the rectangle is just . But, now, we know , so solving for , we get .

Now, our area formula looks like this:

Maximizing the area, we get: