![\begin{aligned} 100 & = \frac{3\sqrt{3}}{2} \cdot s^2 \end{aligned}](/tex.php?f=\begin{aligned} 100 & = \frac{3\sqrt{3}}{2} \cdot s^2 \end{aligned})
we want to isolate s first. if we multiply both sides by the reciprocal of the coefficient on s, which is
![\dfrac{2}{3\sqrt{3}}](/tex.php?f=\dfrac{2}{3\sqrt{3}})
then on the right side, we will get the coefficient canceled out.
![\begin{aligned} 100 & = \frac{3\sqrt{3}}{2} \cdot s^2 \\ \frac{2} {3\sqrt{3}}\cdot 100 & = \frac{2}{3\sqrt{3}} \cdot \frac{3\sqrt{3}}{2} \cdot s^2 \\ \frac{2 \cdot 100} {3\sqrt{3}}& = \frac{2 \cdot 3\sqrt{3}}{2 \cdot 3\sqrt{3}} \cdot s^2 \\ \frac{200} {3\sqrt{3}}& = \frac{1}{1} \cdot s^2 \\ \frac{200} {3\sqrt{3}}& =s^2 \\ \end{aligned}](/tex.php?f=\begin{aligned} 100 & = \frac{3\sqrt{3}}{2} \cdot s^2 \\ \frac{2} {3\sqrt{3}}\cdot 100 & = \frac{2}{3\sqrt{3}} \cdot \frac{3\sqrt{3}}{2} \cdot s^2 \\ \frac{2 \cdot 100} {3\sqrt{3}}& = \frac{2 \cdot 3\sqrt{3}}{2 \cdot 3\sqrt{3}} \cdot s^2 \\ \frac{200} {3\sqrt{3}}& = \frac{1}{1} \cdot s^2 \\ \frac{200} {3\sqrt{3}}& =s^2 \\ \end{aligned})
square root both sides
![\begin{aligned} \sqrt{\frac{200} {3\sqrt{3}}}& =\sqrt{s^2} \\ \sqrt{\frac{200} {3\sqrt{3}}}& =\pm s \\ s & = \pm \sqrt{\frac{200} {3\sqrt{3}}} \end{aligned}](/tex.php?f=\begin{aligned} \sqrt{\frac{200} {3\sqrt{3}}}& =\sqrt{s^2} \\ \sqrt{\frac{200} {3\sqrt{3}}}& =\pm s \\ s & = \pm \sqrt{\frac{200} {3\sqrt{3}}} \end{aligned})
ignore the negative square root; lengths cannot be negative.so
![s = \displaystyle\sqrt{\dfrac{200} {3\sqrt{3}}}](/tex.php?f=s = \displaystyle\sqrt{\dfrac{200} {3\sqrt{3}}})
calculator answer is 6.204032 units