To find the length of one side of a square garden with an area of 205 square feet, we can use the formula for the area of a square:
\[ \text{Area} = \text{side}^2. \]
Thus, to find the length of one side:
\[ \text{side} = \sqrt{\text{Area}} = \sqrt{205} \approx 14.32 \text{ feet}. \]
The closest approximate length of one of the sides from the options given (14 feet, 105 feet, or 51 feet) is 14 feet.
Next, we can calculate the perimeter of the square garden using the formula for the perimeter of a square:
\[ \text{Perimeter} = 4 \times \text{side}. \]
Using the side length we approximated:
\[ \text{Perimeter} \approx 4 \times 14.32 \approx 57.28 \text{ feet}. \]
The closest option for the approximate perimeter from the given options (57 feet, 412 feet, 205 feet, or 114 feet) is 57 feet.