Straightforward Multivariable Calculus Max/Min Problem

[CRBK92]

Homework Statement

A 20-inch piece of wire is to be cut into three pieces. From one piece is made a square and from another is made a rectangle with length equal to twice its width. From the third is made an equilateral triangle. How should the wire be cut so that the sum of the three areas is a maximum?

Homework Equations

Square: A=L^2
Rectangle: A=1/2 L^2
Equilateral Triangle: A=√(3/4) L^2

The Attempt at a Solution

Where do I begin?

 

[LCKurtz]

Homework Statement

A 20-inch piece of wire is to be cut into three pieces. From one piece is made a square and from another is made a rectangle with length equal to twice its width. From the third is made an equilateral triangle. How should the wire be cut so that the sum of the three areas is a maximum?

Homework Equations

Square: A=L^2
Rectangle: A=1/2 L^2
Equilateral Triangle: A=√(3/4) L^2

The Attempt at a Solution

Where do I begin?

You might begin by not using the same letter L to represent three different things.