To find the side length of a square given its perimeter, we can use the relationship between the perimeter and the side length. Recall that the perimeter [tex]\( P \)[/tex] of a square is given by:
[tex]\[ P = 4 \times \text{side length} \][/tex]
In this problem, the perimeter is given as [tex]\( 12x + 52 \)[/tex] units. Therefore, we can set up the following equation:
[tex]\[ 12x + 52 = 4 \times \text{side length} \][/tex]
To find the side length, we need to solve for it in this equation. We do this by dividing both sides of the equation by 4:
[tex]\[ \text{side length} = \frac{12x + 52}{4} \][/tex]
Now, we simplify the right side of the equation by dividing each term in the numerator by 4:
[tex]\[ \text{side length} = \frac{12x}{4} + \frac{52}{4} \][/tex]
[tex]\[ \text{side length} = 3x + 13 \][/tex]
Therefore, the expression that represents the side length of the square is:
[tex]\[ 3x + 13 \][/tex]
So, the correct answer is:
[tex]\[ 3x + 13 \][/tex]
