To solve for [tex]\( s \)[/tex] from the given formula [tex]\( V = \frac{1}{5} s^2 h \)[/tex], follow these steps:
1. Start with the given formula:
[tex]\[
V = \frac{1}{5} s^2 h
\][/tex]
2. Isolate [tex]\( s^2 \)[/tex] by multiplying both sides of the equation by 5:
[tex]\[
5V = s^2 h
\][/tex]
3. Next, isolate [tex]\( s^2 \)[/tex] by dividing both sides of the equation by [tex]\( h \)[/tex]:
[tex]\[
s^2 = \frac{5V}{h}
\][/tex]
4. Finally, solve for [tex]\( s \)[/tex] by taking the square root of both sides:
[tex]\[
s = \pm \sqrt{\frac{5V}{h}}
\][/tex]
Since the problem is asking for the possible values of [tex]\( s \)[/tex], and geometric lengths are typically positive, we usually take the positive root in such contexts.
Therefore, the correct answer is:
[tex]\[
s = \sqrt{\frac{5V}{h}}
\][/tex]
So the correct choice from the provided options is:
A. [tex]\(\sqrt{\frac{5V}{h}}\)[/tex]
