The formula to find the area of a circle is
[tex]\begin{gathered} A=\pi r^2 \\ \text{Where r is the radius and A is the area of the circle} \end{gathered}[/tex]
So as you can see, if you have the area of the circle, you can see get the measure of its radius:
[tex]\begin{gathered} A=289\pi m^2 \\ A=\pi r^2 \\ 289\pi m^2=\pi r^2 \\ \text{ Divide by }\pi\text{ from both sides of the equation} \\ \frac{289\pi m^2}{\pi}=\frac{\pi r^2}{\pi} \\ 289m^2=r^2 \\ \text{ Apply square root to both sides of the equation} \\ \sqrt[]{289m^2}=\sqrt[]{r^2} \\ 17m=r \end{gathered}[/tex]
Now that you have the measure of the radius of the circle, you can obtain its circumference using this formula:
[tex]\begin{gathered} C=2\pi r \\ \text{ Where C is the circumference and} \\ \text{r is the radius of the circle} \end{gathered}[/tex]
So, you have
[tex]\begin{gathered} r=17m \\ C=2\pi r \\ C=2\pi(17m) \\ C=34\pi m \end{gathered}[/tex]
Therefore, the correct answer is option B.
