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 perimeter formula for square

A square has 4 equal sides, so perimeter \( P = 4 \times \text{side length} \) (let side length be \( s \)), so \( P = 4s \).

Step2: Solve for side length

Given \( P = 12x + 52 \), we solve \( 4s = 12x + 52 \) for \( s \). Divide both sides by 4: \( s=\frac{12x + 52}{4}\).

Step3: Simplify the expression

Split the fraction: \( s=\frac{12x}{4}+\frac{52}{4}\). Simplify each term: \( \frac{12x}{4}=3x \), \( \frac{52}{4} = 13 \). So \( s = 3x + 13 \).

Answer:

3x + 13 (the option corresponding to this expression, e.g., if it's option C: C. 3x + 13)