A rectangular garden has a length that is 3 times its width. If the perimeter of the garden is 64 meters, find its width.
["How to Calculate the Width of a Rectangular Garden with a 3:1 Length-to-Width Ratio and a 64-Meter Perimeter", "When designing a garden, understanding the relationship between length, width, and perimeter is essential for efficient space planning. One common scenario is when a rectangular garden has a length that is exactly three times its width. If the perimeter of such a garden is 64 meters, determining the width becomes a straightforward but insightful problem. In this article, we walk through the steps to find the width using algebraic and real-world garden planning principles.", "---", "### Understanding the Rectangular Garden Formula", "For any rectangle:", "- Length = $ L $\n- Width = $ W $", "Given the key ratio:\n$$ L = 3W $$", "The formula for the perimeter $ P $ of a rectangle is:\n$$ P = 2L + 2W $$", "Substituting $ L = 3W $ into the perimeter equation:\n$$ 64 = 2(3W) + 2W $$\n$$ 64 = 6W + 2W $$\n$$ 64 = 8W $$", "---", "### Solving for the Width", "Divide both sides by 8:\n$$ W = \frac{64}{8} = 8 \ ext{ meters} $$", "---", "### Verifying the Solution", "With $ W = 8 $ meters, then:\n- $ L = 3 \ imes 8 = 24 $ meters\n- Perimeter = $ 2(24) + 2(8) = 48 + 16 = 64 $ meters ✔", "This confirms the solution is correct.", "---", "### Why This Matters in Garden Design", "Knowing that a garden with a 3:1 length-to-width ratio and a 64-meter perimeter measures 24 meters by 8 meters helps gardeners:", "- Optimize planting layouts based on shape and space\n- Estimate materials like soil, edging, or fencing accurately\n- Integrate the garden seamlessly into the landscape based on proportions", "Having the width clearly determined ensures balanced design and efficient use of space.", "---", "### Summary", "- The ratio: Length = 3 × Width\n- Perimeter = 64 meters\n- Using $ 2L + 2W = 64 $ and $ L = 3W $\n- Width $ W = 8 $ meters\n- Length $ L = 24 $ meters", "This method simplifies landscape planning and demonstrates how mathematical relationships directly support sound gardening decisions.", "---", "Start planning your garden today — knowing dimensions ensures beauty and functionality!"]
