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Given the expression to calculate the square of the radius of an incircle of a triangle is

$r^2 = {\frac{(s-a)(s-b)(s-c)}{s}}$

Given $a,b,r$ are known can the value of $c$ be found out without a quadratic equation ? Here $s$ stands for the semi perimeter which is $s={\frac{a+b+c}{2}}$

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    The quadratic equation is useful, but never required. You can always complete the square instead. In this case, there's no c^2, so it's possible this isn't even a quadratic equation (s^2 does appear in the problem, but you're not solving for s). – 2017-01-19
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    @barrycarter Yes there is $c^2$ just by simplifying the above expression in order to get $c$ as the subject of the formula we land up with $c^2$. Could please show me how you are not ending up with any squares ? – 2017-01-19
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    @barrycarter Please see what $s$ really stands for. – 2017-01-19
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    My mistake, so I'll stick to my first comment: completing the square can always replace the quadratic equation. – 2017-01-19
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    @ng.newbie That equation is a *cubic* in $c\,$, not a quadratic. – 2017-01-19
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    @dxiv Exactly so it is basically an equation of a higher degree than one. Any way I can avoid and directly get the value of $s$ – 2017-01-19
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    @barrycarter I am sorry, but what do you mean by completing the square ? – 2017-01-19
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    @ng.newbie Not that I am aware of. – 2017-01-19
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    @dxiv Any idea what completing the square means ? – 2017-01-19
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    @ng.newbie See [here](https://en.wikipedia.org/wiki/Completing_the_square) for example. It doesn't apply to *cubic* equations, though. – 2017-01-19

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