the one with the greatest [duplicate]
Show that among all the triangles with base b and prefixed perimeter p, the one with the greatest area is the corresponding isosceles triangle.
As an idea to carry out this demonstration I have used Heron's formula
$$ A = \sqrt{s(s-l1)(s-l2)(s-b)} $$
where b is the base, and l1 and l2 the other sides of the triangle. And the goal is to prove that l1 = l2, but I can't get to the result. Can you give me a hand?
The locus for the third vertex is an ellipse with the base vertices as focal points. To maximise area, we have to maximise height …