Question

You have a wire that is 38 cm long. you wish to cut it into two pieces. one piece will be bent into the shape of a square. the other piece will be bent into the shape of a circle. let a represent the total area of the square and the circle. what is the circumference of the circle when a is a minimum?

Answer 1

Circumference + perimeter =38
x = circumference of circle
find r in terms of x
2$\pi$r=x
r=$\frac{x}{2 \pi }$
Area=$\pi$r^2
so..
A=$\pi$($\frac{x}{2 \pi }$)^2
=$\pi$($\frac{x^{2} }{4 \pi ^{2} }$)
=$\frac{x^{2} }{4 \pi }$

(38-x) is perimeter
then 
$\frac{38-x}{4}$
($\frac{38-x}{4}$)^2
$\frac{x^{2} }{4 \pi }$ + ($\frac{38-x}{4}$)^2
then you graph it and it equals
16.716 cm the circumference of the circle