A square has a perimeter of [tex]\(12x + 52\)[/tex] units. Which expression represents the side length of the square in units?

A. [tex]\(x + 4\)[/tex]
B. [tex]\(x + 40\)[/tex]
C. [tex]\(3x + 13\)[/tex]
D. [tex]\(3x + 43\)[/tex]



Answer :

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]