To find the diameter of a circle given its area, we can use the formula for the area of a circle:
\[ A = \pi r^2 \]
where \(A\) is the area and \(r\) is the radius. We need to solve for the radius first, and then we can find the diameter.
Given that the area \(A = 586\) m², we can rearrange the formula to find \(r\):
\[ r^2 = \frac{A}{\pi} \]
\[ r = \sqrt{\frac{A}{\pi}} \]
Now we can substitute the given area:
\[ r = \sqrt{\frac{586}{\pi}} \approx \sqrt{\frac{586}{3.14159}} \approx \sqrt{186.96} \approx 13.67 \text{ m} \]
Now, the diameter \(d\) is twice the radius:
\[ d = 2r = 2 \times 13.67 \approx 27.34 \text{ m} \]
To the nearest meter, the diameter is approximately 27 m.
The length of the diameter to the nearest meter is 27 m.