SOLUTION: A length of wire is cut into two pieces, one of which is bent to form a circle, the other a square. How should the wire be cut if the area enclosed by the two curves is to be a mi

Question 199429: A length of wire is cut into two pieces, one of which is bent to form a circle, the other a square. How should the wire be cut if the area enclosed by the two curves is to be a minimum?
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let the total length of the wire =
Let the length of a side of the square =
The area of the square will be
The perimeter of the square will be
The perimeter of the circle will be
Let the perimeter of the circle =
Let the radius =

Let area of circle =

The total area is:

Multiply both sides by

If I make a minimum, will be a minimum
With a parabola, the minimum occurs at

The perimeter of the square is:

The perimeter of the circle is:

The cut should be made so the lengths of
the two wires are and
Hope I didn't make a mistake- this is the way to do it, though
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