# Question #09700

Oct 30, 2016

Please see the explanation.

#### Explanation:

Please notice that, if you know the area and the value of s, then you have a quadratic with r as the variable:

$\pi {r}^{2} + \pi s r - A = 0$

Divide everything by $\pi$

${r}^{2} + s r - \frac{A}{\pi} = 0$

Using the quadratic formula:

$r = \frac{- s \pm \sqrt{{s}^{2} + 4 \frac{A}{\pi}}}{2}$

Negative numbers do not make sense for a radius, therefore, you should change the $\pm$ to only $+$:

$r = \frac{- s + \sqrt{{s}^{2} + 4 \frac{A}{\pi}}}{2}$