# Maxima and minima problem

1. Aug 6, 2012

### Rush123

The sum of the perimeter of a circle and square is k, where k is some constant. Prove that the
sum of their areas is least when the side of square is double the radius of the circle.
is this way correct?
assume that x is side of square and r is radius of circle
k=4x+2∏r

sum of areas=area of square+area of circle
find critical pt and find 2nd derivative to show its min.

2. Aug 6, 2012

### HallsofIvy

Staff Emeritus
Yes, that will work. What do you get when you that?

3. Aug 6, 2012

### arildno

Let
A(x,r) be the sum total of the areas. Can you set up the expression for A?

Furthermore, by utilizing the condition that the sum of the perimeters equals k, can you eliminate one of the variables in A, so that A depends on one of the variables only, for example as A(x)?