A rectangular garden measures 15 meters in length and 10 meters in width. A path of uniform width is to be built around the garden, increasing the total area to 231 square meters. What is the width of the path?

["Title: How to Calculate the Width of a Garden Path – Solve This 15m x 10m Garden Project", "Creating a beautiful rectangular garden is just the start—adding a uniform walkway around it can transform its look and functionality. Whether you’re planning a peaceful garden stroll or improved accessibility, adding a path with consistent width boosts both aesthetics and utility. Some gardeners wonder: What width should a path be to increase the area of a 15-meter long and 10-meter wide garden—measuring 231 square meters total—to include the path?", "This article walks you through the classic rectangular garden outline problem with a path, explaining step-by-step how to find the uniform path width that results in a total area of 231 square meters.", "---", "### The Garden Basics", "Start with a rectangular garden where:\n- Length = 15 meters\n- Width = 10 meters\n- Original area = 15 × 10 = 150 square meters", "A path of uniform width ( x ) meters surrounds the garden, increasing the total dimensions.", "---", "### Dimensions Including the Path", "With a path surrounding the garden:\n- New length = 15 + 2x (path adds x meters on each side)\n- New width = 10 + 2x (same reasoning)", "The total area now equals:\n[\n(15 + 2x)(10 + 2x) = 231 \ ext{ square meters}\n]", "---", "### Expanding and Solving the Equation", "Expand the left-hand side:\n[\n(15 + 2x)(10 + 2x) = 150 + 30x + 20x + 4x^2 = 4x^2 + 50x + 150\n]", "Set equal to the total area:\n[\n4x^2 + 50x + 150 = 231\n]", "Subtract 231 to form a standard quadratic equation:\n[\n4x^2 + 50x + 150 - 231 = 0\n]\n[\n4x^2 + 50x - 81 = 0\n]", "---", "### Applying the Quadratic Formula", "Use the quadratic formula:\n[\nx = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\n]\nwhere ( a = 4 ), ( b = 50 ), ( c = -81 )", "Calculate discriminant:\n[\nb^2 - 4ac = 50^2 - 4(4)(-81) = 2500 + 1296 = 3796\n]", "Now compute:\n[\nx = \frac{-50 \pm \sqrt{3796}}{8}\n]\nNote: ( \sqrt{3796} \approx 61.43 )", "[\nx = \frac{-50 \pm 61.43}{8}\n]", "Take the positive root (since width must be positive):\n[\nx = \frac{11.43}{8} \approx 1.43 \ ext{ meters}\n]", "---", "### Final Insight", "The uniform path width around the garden—measuring 15 meters by 10 meters—is approximately 1.43 meters to increase the total area to 231 square meters. This detailed calculation ensures your garden expansion remains precise and intentional.", "---", "### Pro Tips for Garden Path Planning", "- Always double-check dimensions with a rough measurement before construction.\n- Use smaller, uniform path width to maintain symmetry and accessibility.\n- Consider using pavers, gravel, or mulch based on desired style and drainage needs.", "---", "Summary\nInitial garden: 15m × 10m = 150 m²\nIncreased total area with path: 231 m²\nPath width ( x \approx 1.43 ) meters", "Adding a balanced, uniform path enhances garden functionality while optimizing space—make the math work for a lush, accessible outdoor retreat."]