1. ## Quadratic equation problem help

Hello, recently I've started to study some simple math problems by myself and I came across following problem:

A rope of 1 meter is cut in two pieces. Part which lenght is x (m) is made into a circle and other part into a square. What is circle's and square's perimeter when their combined area is smallest possible.

Thing I came up with so far is: A(x)=[(1-x)/4]^2+x^2/4pi but can't process from this point, every time I try something it gets really messy and seems wrong. I assume equation is okay, but what is the next step? I tried simplifying it but can't seem to get it into basic form with that pi popping up at every turn. Any help is appreciated.

2. ## Re: Quadratic equation problem help

Rewrite $A(x)$ in the form

$A(x)=\left(\frac{\pi }{\pi +4}-\frac{2 \pi }{\pi +4} x+x^2\right)\frac{\pi +4}{16\pi }$

and put into basic form what's inside the parentheses

3. ## Re: Quadratic equation problem help

p = pi, r = radius of circle, u = side of square, a = combined area

2pr + 4u = 1

pr^2 + u^2 = a