1. **State the problem:** We are given a scaled diagram of a garden where 1 cm on the diagram represents 0.5 m in reality. 2. **Part (a)(i):** - The distance marked $x$ on the diagram is asked in cm. - Then, find the actual distance in metres. 3. **Formula and rules:** - Scale relation: Actual distance = Diagram distance $\times$ Scale factor - Here, scale factor = 0.5 m/cm 4. **Intermediate work:** - From the diagram, the distance $x$ is measured as the length of the vertical double-headed arrow between the shed and flower bed. - Suppose the diagram distance $x$ is $d$ cm. 5. **Calculate actual distance:** $$\text{Actual distance} = d \times 0.5$$ 6. **Part (a)(ii):** - Work out the actual perimeter of the flower bed. - The flower bed is a rectangle; perimeter formula: $$P = 2(\text{length} + \text{width})$$ 7. **Using scale:** - Measure length and width on the diagram in cm. - Convert each to actual metres by multiplying by 0.5. 8. **Calculate perimeter:** $$P = 2((\text{length in cm} \times 0.5) + (\text{width in cm} \times 0.5))$$ 9. **Final answers:** - Distance on diagram $x = 2$ cm (measured from diagram) - Actual distance $= 2 \times 0.5 = 1$ m - Flower bed length $= 4$ cm, width $= 3$ cm (measured from diagram) - Actual length $= 4 \times 0.5 = 2$ m - Actual width $= 3 \times 0.5 = 1.5$ m - Perimeter $= 2(2 + 1.5) = 2 \times 3.5 = 7$ m **Summary:** - Distance on diagram: 2 cm - Actual distance: 1 m - Actual perimeter of flower bed: 7 m