Awire b units long is cut into two pieces. one piece is bent into an equilateral triangle and the other is bent into a circle. if the sum of the areas enclosed by each part is a minimum, what is the length of each part?

If you notice the picture below

if we take "x" amount for the triangle, then the circle will be using "b-x", since the wire is "b" long

now, that's just their perimeter only

anyhow. ..the sum of their lengths will then be 

so... take the derivative of that areas sum, and check the critical points for a minimum, using the first-derivative test

keeping mind that, "b" is a constant, since that matters for taking the derivative

There is no graph to go along with this