1. **State the problem:** Nadia needs to buy guttering to cover the perimeter of an L-shaped roof with given side lengths. 2. **Identify the sides:** The roof has four sides with lengths: 9 m (top horizontal), 7 m (left vertical), 12 m (right vertical), and 4 m (bottom horizontal). 3. **Calculate the total length of guttering needed:** Since the shape is L-shaped, we must find the total perimeter by adding all the outer sides. The missing horizontal segment on the bottom left can be found by subtracting the bottom horizontal segment from the top horizontal segment: $$9 - 4 = 5\text{ m}$$ 4. **Sum all sides:** Total gutter length needed is $$9 + 7 + 5 + 12 + 4 = 37\text{ m}$$ 5. **Determine the number of 3 m lengths needed:** Each length is 3 m, so divide total length by 3: $$\frac{37}{3} = 12.33$$ Since Nadia cannot buy a fraction of a length, she must buy 13 lengths. **Final answer:** Nadia needs to buy **13** lengths of guttering.