Question #09700

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Answer 1 · 2016-10-30T16:23:33

Please see the explanation.

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

$π r^{2} + π s r - A = 0$ $pir^2 + pisr - A = 0$

Divide everything by $π$ $pi$

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

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

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

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