To find the length of one side of the square, we need to determine the square root of the area given. The area of the square is provided as:
\[ x^2 + 4x + 4 \]
First, we can factor this quadratic expression. Noticing that it matches the form of a perfect square trinomial, we rewrite it:
\[ x^2 + 4x + 4 = (x + 2)^2 \]
Thus, we have:
\[ \text{Area} = (x + 2)^2 \]
To find the length of one side of the square, we take the square root of the area:
\[ \text{Side length} = \sqrt{(x + 2)^2} \]
Since \(x + 2\) is a linear expression, the square root will yield:
\[ \text{Side length} = x + 2 \]
Therefore, the expression that represents the length of one side of the square is:
\[ \boxed{x + 2} \]