A rectangular garden has a length that is 3 times its width. If the perimeter of the garden is 64 meters, what is the width of the garden?
["How to Calculate the Width of a Rectangular Garden with a 3:1 Length-to-Width Ratio and a 64-Meter Perimeter", "If you’re designing a rectangular garden where the length is three times the width, and the total perimeter measures 64 meters, determining the width is a straightforward but valuable calculation for effective garden planning. This article walks through the math clearly, helping homeowners, landscapers, and garden enthusiasts solve similar problems with confidence.", "### Understanding the Rectangular Garden Dimensions", "Let’s define the variables first:", "- Let the width of the garden be ( w ) meters.\n- Since the length is 3 times the width, the length is ( 3w ) meters.", "### Using the Perimeter Formula", "The perimeter ( P ) of a rectangle is calculated using the formula:\n[\nP = 2 \ imes (\ ext{Length} + \ ext{Width})\n]\nSubstituting the known values:\n[\n64 = 2 \ imes (3w + w)\n]\nSimplify inside the parentheses:\n[\n64 = 2 \ imes 4w\n]\n[\n64 = 8w\n]\nNow, solve for ( w ):\n[\nw = \frac{64}{8} = 8\n]", "### Final Answer", "The width of the garden is 8 meters.\nThis means the length is ( 3 \ imes 8 = 24 ) meters, and indeed:\n[\n2 \ imes (24 + 8) = 2 \ imes 32 = 64 \ ext{ meters}\n]\n— confirming our calculation is accurate.", "### Practical Application", "Knowing the width enables precise planning for planting layouts, irrigation systems, fencing, and material estimates. Whether you’re expanding your green space or redesigning an existing garden, understanding dimension ratios like 3:1 helps maximize functionality and aesthetics.", "---", "Key Takeaways:\n- Use algebra to express perimeter in terms of one variable.\n- Simplify using the known 3:1 ratio.\n- Always verify with the original perimeter value.\n- A survey width of 8 meters with a 24-meter length perfectly fits a 64-meter perimeter.", "This simple method empowers anyone to tackle garden design and construction projects with confidence."]
