\begin{tabular}{l} 5. If the scale factor of Figure \( A \) to Figure \( B \) is \\ \( 7: 2 \), find the perimeter of Figure \( A \). \\ \( \qquad \begin{array}{l}12 \\ 2 x=245 \\ x=122\end{array} \) \\ \hline\end{tabular}

To find the perimeter of Figure \( A \) given the scale factor of \( 7:2 \) from Figure \( A \) to Figure \( B \), we can follow these steps: 1. **Understand the Scale Factor**: The scale factor \( 7:2 \) means that for every 7 units in Figure \( A \), there are 2 units in Figure \( B \). This can be expressed as: \[ \frac{A}{B} = \frac{7}{2} \] 2. **Find the Perimeter of Figure \( B \)**: The problem provides the equation \( 2x = 245 \). We can solve for \( x \): \[ x = \frac{245}{2} = 122.5 \] This value \( x \) represents the perimeter of Figure \( B \). 3. **Calculate the Perimeter of Figure \( A \)**: Using the scale factor, we can find the perimeter of Figure \( A \) by setting up the proportion: \[ \frac{A}{B} = \frac{7}{2} \] Substituting \( B = 122.5 \): \[ \frac{A}{122.5} = \frac{7}{2} \] 4. **Cross-Multiply to Solve for \( A \)**: \[ 2A = 7 \times 122.5 \] Now calculate \( 7 \times 122.5 \): \[ 7 \times 122.5 = 857.5 \] Therefore: \[ 2A = 857.5 \] Dividing both sides by 2 gives: \[ A = \frac{857.5}{2} = 428.75 \] Thus, the perimeter of Figure \( A \) is \( 428.75 \).