A wire is divided into two parts. One part is shaped into a square, and the other part is shaped into a circle. Let r be the ratio of the circumference of the circle to the perimeter of the square when the sum of the areas of the square and circle is minimized. Find r.
Derivative and area of circle and square
The Attempt at a Solution
So I figure I have a wire y since I don't know the length cut it into two pieces x for the square and y-x for the circle. Area of the square is (x/4)^2 While y-x=2pir, r=y-x/2pi So area of circle is (y-x/2pi)^2
Now I want to minimize the total area by taking the derivative and setting it equal to zero. My problem is the y and this doesn't seem right. Any help is appreciated I still struggle with these word problems