5. If the scale factor of Figure \( A \) o Figure \( B \) is \( 7: 2 \), find the perimeter of Figure \( A \). \( x=12+9(2)+5=35 \) \( x=245 \) \( 2 x=\frac{12}{2} \)

Certainly! Let's break down the problem step by step to ensure clarity. ### **Problem Statement** **Given:** - The scale factor from Figure **A** to Figure **B** is \( 7:2 \). - Some calculations involving \( x \) are provided: - \( x = 12 + 9(2) + 5 = 35 \) - \( x = 245 \) - \( 2x = \frac{12}{2} \) **Objective:** Find the perimeter of Figure **A**. --- ### **Understanding Scale Factors** When dealing with similar figures, the scale factor relates corresponding linear measurements (like perimeters) proportionally. Specifically: - If the **scale factor from A to B** is \( \frac{7}{2} \), then: - **Perimeter of A** : **Perimeter of B** = \( 7 : 2 \) This means: \[ \frac{\text{Perimeter of A}}{\text{Perimeter of B}} = \frac{7}{2} \] --- ### **Interpreting the Given Calculations** Let's interpret the provided calculations to find the perimeter of Figure **A**. 1. **Calculating \( x \):** \[ x = 12 + 9(2) + 5 = 12 + 18 + 5 = 35 \] - Here, \( x \) likely represents the **perimeter of Figure B**. 2. **Scaling Up to Find Perimeter of A:** - Given the scale factor \( \frac{7}{2} \), to find the perimeter of **A** when **B's** perimeter is 35: \[ \text{Perimeter of A} = \frac{7}{2} \times \text{Perimeter of B} = \frac{7}{2} \times 35 = 122.5 \] 3. **Alternative Calculation:** - It seems there's another step where \( x = 245 \). This could be interpreted as: \[ 35 \times 7 = 245 \] - Here, multiplying **B's** perimeter by 7 directly gives 245, which suggests a different interpretation of the scale factor or another part of the problem not fully detailed. 4. **Final Step:** - The step \( 2x = \frac{12}{2} \) simplifies to: \[ 2x = 6 \implies x = 3 \] - This step is unclear without additional context. It might relate to another dimension or aspect of the figures. --- ### **Conclusion** Based on the initial calculation: - If **Figure B's** perimeter is **35**, and the scale factor from **A** to **B** is \( 7:2 \), then: \[ \text{Perimeter of A} = \frac{7}{2} \times 35 = 122.5 \] However, if following the later step where \( x = 245 \), it suggests that: - The perimeter of **A** is **245**. **Final Answer:** The perimeter of Figure **A** is **245** units. --- ### **Note** It's essential to ensure all steps and given values are consistent and clearly defined. If there's additional context or specific parts of the problem statement that weren't included, please provide them for a more accurate and comprehensive solution.