Extreame values word problem

[Guest]

I don't know how to do this question and need help:

13. A piece of wire 40cm long is cut into two pieces. One piece is bent into the shape of a square and the other is bent into the shape of a circle. How should the wire be cut so that the total area enclosed is
(a) a maximum? b) a Minimum


I'm not sure how you do this since there are two shapes.
Help! >.<

Thanks a lot for the help and time

 

[stapel]

Hint: If the wire for the square is of length "x", then what is the remaining length of wire for the circle?

Eliz.

 

[galactus]

\(\displaystyle x+y=40\)

\(\displaystyle 2{\pi}r=x\)

\(\displaystyle 4s=y\)

Therefore, \(\displaystyle r=\frac{x}{2{\pi}}\)

and \(\displaystyle s=\frac{y}{4}\)

\(\displaystyle A={\pi}r^{2}+s^{2}\)

Some subbing here, some differentiating there, and you have it.

 

[sigma]

Ugh! Extrema problems don't get any worse than this type of question. This question is very difficult. What you have to do is differentiate a messy equation with roots and everything. Its not so much setting up the equation but the algebraic manipulation takes forever especially if the circle was a triangle.