We need to set up the equation to calculate the perimeter of the rectangle and then compare it to $\(x+4\)$.
Perimeter of rectangle: $\(2(x+8+x) \Rightarrow 2(2 x +8) \Rightarrow 4 x+16\)$
Since the square has the same perimeter as the rectangle, we know that the perimeter divided by 4 is the length of any side of the square. So the length of a side of square $A$ :

$$
\(\frac{(4 x+16)}{4}=x+4\)
$$

C is the answer