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Thread: Quadratic equation problem help

  1. #1
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    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.
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  2. #2
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    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
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  3. #3
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    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
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