Pentagon formed by placing isosceles triangle on rectangle Perimeter = 10 Sides that maximize area?

Описание к видео Pentagon formed by placing isosceles triangle on rectangle Perimeter = 10 Sides that maximize area?

This video shows how the method of Lagrange Multipliers can be used to optimize a function of 3 variables with 1 constraint.
Problem:
A pentagon is formed by placing an isosceles triangle on a rectangle, as shown in the diagram. If the perimeter of the pentagon is 10 in., find the lengths of the sides of the pentagon that will maximize the area of the pentagon.

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