MI Listen MODELING REAL LIFE Your family decides to put a rectangular patio in your backyard, similar to the shape of your backyard. Your backyard has a length of 45 feet and a width of 20 feet. The length of your new patio is 18 feet. Find the perimeter of your backyard and the perimeter of the patio. Backyard perimeter: \( \square \) feet Patio perimeter: \( \quad \) feet

To find the perimeters of both the backyard and the patio, we can use the formula for the perimeter \( P \) of a rectangle, which is given by: \[ P = 2 \times (L + W) \] where \( L \) is the length and \( W \) is the width. ### Step 1: Calculate the perimeter of the backyard Given: - Length of the backyard \( L = 45 \) feet - Width of the backyard \( W = 20 \) feet Using the perimeter formula: \[ P_{\text{backyard}} = 2 \times (45 + 20) \] Now, let's calculate this: \[ P_{\text{backyard}} = 2 \times 65 = 130 \text{ feet} \] ### Step 2: Calculate the perimeter of the patio Given: - Length of the patio \( L = 18 \) feet - The width of the patio is the same as the width of the backyard, which is \( W = 20 \) feet. Using the perimeter formula: \[ P_{\text{patio}} = 2 \times (18 + 20) \] Now, let's calculate this: \[ P_{\text{patio}} = 2 \times 38 = 76 \text{ feet} \] ### Final Answers - Backyard perimeter: \( 130 \) feet - Patio perimeter: \( 76 \) feet Thus, the answers are: - Backyard perimeter: \( 130 \) feet - Patio perimeter: \( 76 \) feet