A rectangular garden measures 24 meters by 15 meters. A path of uniform width is to be built inside the garden along its edges, reducing the area available for planting to 252 square meters. What is the width of the path?

["Title: How to Calculate the Width of a Uniform Garden Path – A 24m x 15m Garden Case Study", "---", "Introduction\nCreating a beautiful and functional rectangular garden often involves planning beyond just planting borders and flowers. Many gardeners choose to incorporate a walking path around the inner edges to enhance accessibility and aesthetics. However, a path reduces the usable planting area—especially in narrower gardens. In this article, we’ll explore a practical scenario: a garden measuring 24 meters by 15 meters, with a uniform narrow path built inside along all edges, leaving just 252 square meters for planting. We’ll calculate the precise width of the path, explaining how to determine uniform dimensions from overall garden measurements.", "---", "Understanding the Problem\nWe start with a rectangular garden of size 24 meters in length and 15 meters in width, giving a total area of:", "[\n24 \ imes 15 = 360 \ ext{ square meters}\n]", "A uniform width (x) meters of path is to be constructed inside along all edges. This removes a smaller inner rectangle where planting occurs. The remaining planting area equals 252 square meters, so the area occupied by the path is:", "[\n360 - 252 = 108 \ ext{ square meters}\n]", "Now, we determine the inner planting region’s dimensions. Since the path runs along all edges, the inner planting rectangle is reduced on both sides by (x) meters in length and (x) meters in width. Therefore, the inner planting area is:", "[\n\ ext{Height} = 15 - 2x\n]\n[\n\ ext{Length} = 24 - 2x\n]", "The area of this inner rectangle is:", "[\n(24 - 2x)(15 - 2x) = 252\n]", "---", "Solving the Equation\nWe expand and solve the quadratic equation:", "[\n(24 - 2x)(15 - 2x) = 252\n]\n[\n24 \cdot 15 - 24 \cdot 2x - 15 \cdot 2x + 4x^2 = 252\n]\n[\n360 - 48x - 30x + 4x^2 = 252\n]\n[\n4x^2 - 78x + 360 = 252\n]\n[\n4x^2 - 78x + 108 = 0\n]", "Divide through by 2 to simplify:", "[\n2x^2 - 39x + 54 = 0\n]", "Now apply the quadratic formula:", "[\nx = \frac{39 \pm \sqrt{(-39)^2 - 4 \cdot 2 \cdot 54}}{2 \cdot 2}\n]\n[\nx = \frac{39 \pm \sqrt{1521 - 432}}{4}\n]\n[\nx = \frac{39 \pm \sqrt{1089}}{4}\n]\n[\nx = \frac{39 \pm 33}{4}\n]", "This gives two solutions:", "[\nx = \frac{39 + 33}{4} = \frac{72}{4} = 18 \quad (\ ext{too large—doesn’t fit garden dimensions})\n]\n[\nx = \frac{39 - 33}{4} = \frac{6}{4} = 1.5 \ ext{ meters}\n]", "---", "Verifying the Solution\nWith (x = 1.5), the inner planting area becomes:", "[\n(24 - 2 \ imes 1.5) \ imes (15 - 2 \ imes 1.5) = (24 - 3) \ imes (15 - 3) = 21 \ imes 12 = 252 \ ext{ square meters}\n]", "This confirms the solution accurately reflects the given planting area.", "---", "Why This Matters\nUnderstanding how path width affects usable garden space helps optimize layout and maximize productivity. In this case, a 1.5-meter-wide path effectively reduces planting area by 108 square meters within a 24 × 15 meter garden. Such calculations are essential when designing sustainable, functional garden spaces where form and function coexist.", "---", "Final Answer:\nThe width of the uniform path is 1.5 meters.", "---", "Call to Action:\nPlan your next garden project with precision—use our guide to calculate path widths and balance beauty with practicality. Get your garden layout optimized today!", "---", "Keywords: rectangular garden, garden path width, internal path calculation, planting area reduction, garden design, 24m by 15m garden, uniform path, planting space optimization", "---", "Embrace smart gardening with expert calculations—where every centimeter counts. 🌿"]