A rectangular garden is 30 meters long and 20 meters wide. A path of uniform width surrounds the garden. If the total area of the garden and the path is 936 square meters, what is the width of the path?
["Title: How to Calculate the Width of a Uniform Garden Path Surrounding a Rectangular Garden", "Creating a rectangular garden doesn’t have to stop at just the growing space. Often, a neat, uniform path surrounds the garden to improve aesthetics and accessibility. If you're planning a garden that measures 30 meters long and 20 meters wide, and the total area including a surrounding path is 936 square meters, you might wonder: What is the width of the path? This SEO-rich article guides you step-by-step through the math and logic to determine the exact path width.", "---", "### Understanding the Problem", "You are given:", "- Length of the garden: 30 meters\n- Width of the garden: 20 meters\n- Total area (garden + path): 936 m²\n- The path surrounds the garden uniformly — meaning it adds equal width all around", "Let the uniform width of the path be x meters. The path surrounds the entire garden, so it adds 2x meters to both the length and the width of the garden.", "---", "### Step 1: Determine the Outer Dimensions", "With the path added uniformly:", "- Total length = garden length + 2 × path width = 30 + 2x\n- Total width = garden width + 2 × path width = 20 + 2x", "The total area is:", "[\n\ ext{Total area} = (\ ext{Length}) \ imes (\ ext{Width}) = (30 + 2x)(20 + 2x) = 936\n]", "---", "### Step 2: Set Up the Equation", "[\n(30 + 2x)(20 + 2x) = 936\n]", "Expand the left-hand side using the distributive property (FOIL method):", "[\n30 \cdot 20 + 30 \cdot 2x + 20 \cdot 2x + 2x \cdot 2x = 936\n]\n[\n600 + 60x + 40x + 4x^2 = 936\n]\n[\n4x^2 + 100x + 600 = 936\n]", "---", "### Step 3: Simplify the Quadratic Equation", "Subtract 936 from both sides:", "[\n4x^2 + 100x + 600 - 936 = 0\n]\n[\n4x^2 + 100x - 336 = 0\n]", "To simplify, divide the entire equation by 4:", "[\nx^2 + 25x - 84 = 0\n]", "---", "### Step 4: Solve the Quadratic Using Factoring", "We now solve:", "[\nx^2 + 25x - 84 = 0\n]", "Look for two numbers that multiply to -84 and add to 25.", "Those numbers are 28 and -3:", "[\n(x + 28)(x - 3) = 0\n]", "Set each factor equal to zero:", "[\nx + 28 = 0 \quad \Rightarrow \quad x = -28 \quad (\ ext{not physically valid})\n]\n[\nx - 3 = 0 \quad \Rightarrow \quad x = 3\n]", "---", "### Step 5: Confirm and Interpret the Result", "The only valid solution is x = 3 meters.", "- The path width is 3 meters on all sides.\n- Total dimensions including the path:\n - Length: 30 + 2×3 = 36 meters\n - Width: 20 + 2×3 = 26 meters\n - Area: 36 × 26 = 936 m² ✅", "---", "### Why This Matters: Real-World Applications and SEO Insights", "When designing garden spaces, knowing how path width affects total area is crucial for planning materials, budgeting, and user experience. Using correct mathematical models helps avoid costly mistakes and ensures functional design.", "Key SEO Keywords:\n- Rectangular garden path width calculation\n- How to calculate garden path dimensions\n- Uniform path surrounding rectangular garden\n- Area of garden plus path formula\n- Solve rectangular garden path problem", "For bloggers and landscape architects, mastering these calculations enhances credibility and improves search visibility for “garden path width” or “rectangular garden total area.”", "---", "### Final Answer", "The width of the uniformly surrounding path is 3 meters.", "---", "Happy gardening — and may your path be both beautiful and precisely measured!"]
