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 400 square meters. What is the width of the walkway?

["Title: Determine the Walkway Width Around a 25m × 10m Rectangular Swimming Pool with 400m² Total Area", "When designing a family pool, one common goal is maximizing space while maintaining aesthetic balance—especially when incorporating a walkway. Consider a rectangular swimming pool measuring 25 meters long and 10 meters wide. A uniform walkway surrounds the pool, increasing the total area to 400 square meters. This article explains how to calculate the precise width of the walkway, empowering homeowners and designers to create well-proportioned outdoor spaces.", "---", "### Understanding the Pool and Walkway Dimensions", "The pool itself measures:", "- Length (L): 25 meters\n- Width (W): 10 meters", "Without the walkway, the pool occupies:\nArea_pool = 25 × 10 = 250 m²", "The total area, including the walkway, is 400 m², meaning the walkway covers:\nTotal area − Pool area = 400 − 250 = 150 m²", "---", "### Setting Up the Variables", "Let x be the uniform width of the walkway surrounding the pool in all directions. Since the walkway adds space equally to both sides:", "- Total length of the entire area = 25 + 2x\n- Total width of the entire area = 10 + 2x", "The total area becomes:\n[\n(25 + 2x)(10 + 2x) = 400\n]", "---", "### Expanding and Solving the Equation", "Expand the left-hand side:", "[\n(25 + 2x)(10 + 2x) = 250 + 50x + 20x + 4x^2 = 250 + 70x + 4x^2\n]", "Set equal to 400:", "[\n250 + 70x + 4x^2 = 400\n]", "Subtract 400 from both sides:", "[\n4x^2 + 70x + 250 − 400 = 0 \Rightarrow 4x^2 + 70x − 150 = 0\n]", "---", "### Simplifying the Quadratic Equation", "Divide the entire equation by 2 to simplify:", "[\n2x^2 + 35x − 75 = 0\n]", "Use the quadratic formula:\n[\nx = \frac{−b \pm \sqrt{b^2 − 4ac}}{2a}, \quad \ ext{where } a = 2,\ b = 35,\ c = −75\n]", "Calculate the discriminant:\n[\n\Delta = 35^2 − 4(2)(−75) = 1225 + 600 = 1825\n]", "[\nx = \frac{−35 \pm \sqrt{1825}}{4}\n]", "Approximate √1825:\n[\n\sqrt{1825} \approx 42.72\n]", "So:", "[\nx = \frac{−35 + 42.72}{4} = \frac{7.72}{4} \approx 1.93 \quad \ ext{(only the positive root is valid)}\n]", "---", "### Final Answer", "The width of the uniform walkway is approximately 1.93 meters, or more precisely:\n[\n\boxed{\frac{−35 + \sqrt{1825}}{4} \approx 1.93\ \ ext{meters}}\n]", "---", "### Practical Insights and Design Considerations", "- A 1.93-meter-wide walkway provides ample space for comfortable movement without overwhelming the pool’s surroundings.\n- Exact measurements help with paving materials, costs, and ensuring safe, accessible edges.\n- For construction, rounding to 2 meters is often preferred for ease, bringing total area to (27 × 12 = 324 m²), slightly over 400—so slight fine-tuning might be needed depending on landscape goals.", "---", "Bottom line: A precisely measured walkway of about 1.93 meters enhances both function and beauty around a 25m × 10m pool, confirming optimal space utilization in residential water features.", "---", "Keywords: rectangular swimming pool, walkway width, pool area calculation, 25m × 10m pool, frequency question walkway, outdoor pool design, uniform walkway math, 400 square meter total area"]