A wire 8 meters long is cut into two pieces. One piece is bent into a equilateral triangle for a frame for a stained glass ornament, while the other piece is bent into a circle for a TV antenna. To reduce storage space, where should the wire be cut to minimize the total area of both figures? Give the length of wire used for each:
Triangle:
Circle:
Where should it be cut to maximize the: Triangle:
Circle

Question

A wire 8 meters long is cut into two pieces. One piece is bent into a equilateral triangle for a frame for a stained glass ornament, while the other piece is bent into a circle for a TV antenna. To reduce storage space, where should the wire be cut to minimize the total area of both figures? Give the length of wire used for each: 
Triangle: 
Circle: 
Where should it be cut to maximize the: Triangle: 
Circle

anonymous · Answer

A Mathematica calculation and plot is attached.

anonymous · Answer

Nice. Thanks.

anonymous · Answer

@wrstlr3232
Your welcome and thank you for the medal.

Don't know why some of the high end talent on this site did not solve this problem for you, earlier.

anonymous · Answer

By the way, I turned 80 years old last August.
Without the assistance of Mathematica I would not be able to calculate anything.  Cannot integrate x^2 by pencil and paper.