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## Homework Statement

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.

## Homework Equations

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