A rectangular swimming pool is 25 meters long and 10 meters wide. A walkway of uniform width surrounds the pool, increasing the total area to 600 square meters. Find the width of the walkway.
["What’s the Width of the Uniform Walkway Surrounding a 25m × 10m Rectangular Pool?", "A rectangular swimming pool measuring 25 meters long and 10 meters wide is often enhanced with a surrounding walkway to create a spacious, functional outdoor space. When a uniform walkway of equal width surrounds the pool, the total area expands to 600 square meters. This article explores how to calculate the precise width of the walkway and its practical benefits.", "---", "Understanding the Pool and Walkway Geometry", "Let’s denote the uniform width of the walkway as x meters. Since the walkway surrounds the pool evenly, it adds the same distance (x meters) on all sides:", "- Pool length: 25 meters → Total length including walkway = 25 + 2x\n- Pool width: 10 meters → Total width including walkway = 10 + 2x", "The total area of the pool plus walkway is then given by:", "[\n\ ext{Total Area} = (25 + 2x)(10 + 2x)\n]", "We know the total area equals 600 square meters:", "[\n(25 + 2x)(10 + 2x) = 600\n]", "---", "Expanding and Solving the Equation", "First, expand the left-hand side:", "[\n(25 + 2x)(10 + 2x) = 25 \cdot 10 + 25 \cdot 2x + 2x \cdot 10 + 2x \cdot 2x = 250 + 50x + 20x + 4x^2 = 4x^2 + 70x + 250\n]", "Set this equal to 600:", "[\n4x^2 + 70x + 250 = 600\n]", "Subtract 600 from both sides:", "[\n4x^2 + 70x + 250 - 600 = 0 \implies 4x^2 + 70x - 350 = 0\n]", "Simplify by dividing all terms by 2:", "[\n2x^2 + 35x - 175 = 0\n]", "---", "Applying the Quadratic Formula", "Use the quadratic formula:", "[\nx = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\n]", "Where:\n- ( a = 2 ),\n- ( b = 35 ),\n- ( c = -175 )", "Calculate the discriminant:", "[\n\Delta = 35^2 - 4(2)(-175) = 1225 + 1400 = 2625\n]", "Now compute:", "[\nx = \frac{-35 \pm \sqrt{2625}}{4}\n]", "Simplify (\sqrt{2625}):\n[\n2625 = 25 \ imes 105 = 25 \ imes 15 \ imes 7 = 5^2 \ imes 3 \ imes 5 \ imes 7 = 5^2 \ imes 3 \ imes 7\n\Rightarrow \sqrt{2625} = 5\sqrt{105} \approx 51.23\n]", "So:", "[\nx = \frac{-35 \pm 51.23}{4}\n]", "Take the positive root (width cannot be negative):", "[\nx = \frac{-35 + 51.23}{4} = \frac{16.23}{4} \approx 4.06 \ ext{ meters}\n]", "---", "Verification", "Total length = 25 + 2(4.06) = 33.12 m\nTotal width = 10 + 2(4.06) = 18.12 m\nTotal area = 33.12 × 18.12 ≈ 599.9 ≈ 600 m² ✅", "---", "Why a Walkway of ~4.06 Meters Is Practical", "Beyond calculations, a walkway this width transforms the pool environment—providing comfort for sunbathing, relaxing, and easy access around the pool. With a length much greater than its width, the walkway maximizes outdoor usability while seamlessly integrating with the pool’s rectangular shape.", "---", "Conclusion", "A rectangular pool measuring 25 meters by 10 meters, with a uniform walkway of width approximately 4.06 meters, increases the total area to 600 square meters. This precise calculation ensures design accuracy and enhances outdoor functionality, turning a simple pool into a complete residential retreat.", "---", "Key Takeaways:", "- Given: Pool area = 25 × 10 = 250 m²\n- Total area with walkway = 600 m²\n- Walkway width = ( x ) → total dimensions: (25 + 2x) × (10 + 2x) = 600\n- Solving yields: walkway width ≈ 4.06 meters", "Planning your pool with a properly sized walkway improves both aesthetics and utility—ideal for homeowners designing a new outdoor space.", "---", "Keywords: rectangular pool walkway area calculation, pool with walkway dimensions, how wide is a pool walkway, 25m pool 10m pool total area 600m2, solve pool walkway width, pool surrounding walkway math"]
