1. **State the problem:** We need to find the total amount of rope required to rope off two excavation sites, Site A and Site B. 2. **Given data:** - Site A is rectangular with length $60$ meters and width $40$ meters. - Site B is similar in shape to Site A and has a length of $45$ meters. 3. **Important rule:** Since Site B is similar to Site A, the ratio of corresponding sides is the same. The width of Site B can be found using the similarity ratio. 4. **Calculate the width of Site B:** $$\text{Similarity ratio} = \frac{\text{Length of Site B}}{\text{Length of Site A}} = \frac{45}{60} = \frac{3}{4}$$ $$\text{Width of Site B} = \frac{3}{4} \times 40 = 30 \text{ meters}$$ 5. **Calculate the perimeter of Site A:** $$P_A = 2 \times (60 + 40) = 2 \times 100 = 200 \text{ meters}$$ 6. **Calculate the perimeter of Site B:** $$P_B = 2 \times (45 + 30) = 2 \times 75 = 150 \text{ meters}$$ 7. **Calculate total rope needed:** $$\text{Total rope} = P_A + P_B = 200 + 150 = 350 \text{ meters}$$ **Final answer:** The total rope needed for both sites is $350$ meters.