Question

a square has a perimeter of 12x + 52 units. which expression represents the side length of the square in units?
○ x + 4
○ x + 40
○ 3x + 13
○ 3x + 43

Explanation:

Step1: Recall the formula for the perimeter of a square.

The perimeter \( P \) of a square is given by \( P = 4s \), where \( s \) is the side length of the square. So, to find the side length \( s \), we can solve the formula for \( s \), which gives \( s=\frac{P}{4} \).

Step2: Substitute the given perimeter into the formula.

We are given that the perimeter \( P = 12x + 52 \). Substituting this into the formula for \( s \), we get \( s=\frac{12x + 52}{4} \).

Step3: Simplify the expression.

We can split the fraction: \( \frac{12x + 52}{4}=\frac{12x}{4}+\frac{52}{4} \). Simplifying each term, \( \frac{12x}{4} = 3x \) and \( \frac{52}{4}=13 \). So, \( s = 3x + 13 \).

Answer:

3x + 13 (corresponding to the option "3x + 13")