Two sides of a square are represented by \( (x+9) \) and \( (6 x-1) \). What is the perimeter of the square? Show all work. POSSIBLE

To find the perimeter of the square, we'll follow these steps: 1. **Understand the Properties of a Square** - A square has four equal sides. - Therefore, all four side lengths are congruent (equal in length). 2. **Set Up the Equation** You're given two expressions representing the sides of the square: \[ \text{Side 1} = x + 9 \] \[ \text{Side 2} = 6x - 1 \] Since all sides of a square are equal: \[ x + 9 = 6x - 1 \] 3. **Solve for \( x \)** Let's solve the equation step-by-step to find the value of \( x \): \[ x + 9 = 6x - 1 \] - **Step 1:** Subtract \( x \) from both sides to get all \( x \)-terms on one side: \[ x + 9 - x = 6x - 1 - x \] \[ 9 = 5x - 1 \] - **Step 2:** Add 1 to both sides to isolate the \( x \)-term: \[ 9 + 1 = 5x - 1 + 1 \] \[ 10 = 5x \] - **Step 3:** Divide both sides by 5 to solve for \( x \): \[ \frac{10}{5} = \frac{5x}{5} \] \[ 2 = x \] So, \( x = 2 \). 4. **Find the Length of One Side** Now, substitute \( x = 2 \) back into one of the side expressions to find the length of one side of the square. We'll use \( x + 9 \): \[ \text{Side} = x + 9 = 2 + 9 = 11 \text{ units} \] 5. **Calculate the Perimeter** The perimeter \( P \) of a square is four times the length of one side: \[ P = 4 \times \text{Side} = 4 \times 11 = 44 \text{ units} \] **Answer:** The perimeter of the square is **44 units**.