I'm out of ideas on this one!!! I need help!

[masterofkenpo]

So for the past week we have started optimization problems. I am not a very strong math student and am having trouble. :? We just got a problem in class that I really don't know how to solve. I hope someone can help me. Here goes:

Question - A piece of wire 10 meters long is cut into two pieces. One piece is bent into the shape of a circle; the other is made into an equilateral triangle. Determine where to make the cut as to (a) minimize the enclosed area and (b) maximize the enclosed area.

Note: The cut may be trivially made and an endpoint so that one piece is 10 meters and the other is 0 meters.



If anyone can help me out with this problem I would greatly appreciate it. I'm running out of time and willpower.

 

[stapel]

The total length is 10. One piece has length, say, "x". How long then is the other piece?

What is the area formula for a circle with circumference "C"? Can you use this to relate the length of the wire to the area?

What is the area formula for an equilateral triangle with perimeter "P"? Can you use this to relate the remaining length of wire to the area?

Eliz.