How Should Wire Be Cut to Minimize Combined Area of Circle and Square?

[daykie08]

Homework Statement

A piece of wire 10ft long is cut into two pieces. One piece is bent into the shape of a circle and the other into the shape of a square. How should the wire be cut so that the combined area of the two figures is as small as possible

Homework Equations

The Attempt at a Solution

radius=r and side of the square=s
answer: r = 5/(pi+4) and s =10/(pi+4)

I have the answer but I don't know how should I do it... Please help

 

[courtrigrad]

A piece of wire 10ft long is cut into two pieces. One piece is bent ito the shape of a circle and the other into the shape of a square. How should the wire be cut so that the combined area of the two figures is as small as possible

should that be

A piece of wire 10ft long is to be cut into two pieces. One piece is bent ito the shape of a circle and the other into the shape of a square. How should the wire be cut so that the combined area of the two figures is as small as possible

 

[radou]

Write down the equations for the area of a circle and the area of a square. The area of the circle has the parameter r (the radius) and the area of the square has the parameter s (the side of the square). Find the connection between these parameters and between the parameters a and b which represent the two cut pieces of the wire. Further on, create a sum A(a, b) = A1(a) + A2(b). Then plug in the relation between a and b (i.e. a + b = 10). Then you'll get the total area in a single variable, A(a) = ... (or A(b), doesn't matter). Differentiate with respect to that variable and set equal to zero.