Question

If the two equal sides of an isosceles triangle are 2 cm long, find the length of the third side thatmaximizes the area of the triangle.

Answer 1

The area is a function of the apex angle β according to
  Area = (1/2)(2 cm)²×sin(β)

This will be a maximum for β = 90°. The corresponding length of the third side is
  2√2 cm
  ≈ 2.2828 cm