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 can rearrange this formula to find the radius:
\[ r = \sqrt{\frac{A}{\pi}} \]
Once we find the radius, we can find the diameter using the formula:
\[ d = 2r \]
Given that the area \( A = 586 , m^2 \):
\[ r = \sqrt{\frac{586}{\pi}} \approx \sqrt{\frac{586}{3.14159}} \approx \sqrt{186.78} \approx 13.66 , m \]
Now, we can find the diameter:
\[ d = 2r \approx 2 \cdot 13.66 \approx 27.32 , m \]
Rounding this to the nearest meter gives:
\[ d \approx 27 , m \]
So the length of the diameter to the nearest meter is 27 m.