SOLUTION: A Wire Length L Is To Cut Into Two Pieces, One Of Which Is To Be Bent Into The Shape Of A Circle And The Other Into The Shape Of An Equilateral Triangle. Find The Length Of Each Pi

Question 1019815: A Wire Length L Is To Cut Into Two Pieces, One Of Which Is To Be Bent Into The Shape Of A Circle And The Other Into The Shape Of An Equilateral Triangle. Find The Length Of Each Piece So That The Sum Of The Enclosed Areas Is A Minimum

Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
= radius of the circle
= side of the triangle
length of the wire before cutting it

= length of wire used for the circle
= length of wire used for the triangle
<-->

Area of the triangle =
Area of the circle =
Total area =

That is a quadratic function.
Quadratic functions of the form with
have a minimum at .
In the case of ,
, , and ,
so the minimum is at

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