A rectangular garden has a length of 30 meters and a width of 20 meters. A path of uniform width is built around the garden, increasing the total area to 1,000 square meters. What is the width of the path?

["A rectangular garden has a length of 30 meters and a width of 20 meters. A path of uniform width is built around the garden, increasing the total area to 1,000 square meters. What is the width of the path?", "Creating a functional and beautiful outdoor space often combines practicality with aesthetics—like designing a rectangular garden with a surrounding path that enhances both layout and experience. This perfectly balances open green space with accessible walkways, a growing trend among homeowners seeking outdoor retreats without sacrificing garden integrity. In a market where curated outdoor living drives both home value and daily wellness, adding a uniform Border around a rectangular garden isn’t just about appearance—it’s about maximizing space efficiently. But when the garden and path together form a 1,000-square-meter footprint, figuring out the path’s width becomes a precise calculation shaped by simple geometry.", "Why Is This Pattern Gaining Attention in the US? \nWith rising interest in sustainable living and modular outdoor design, uniform garden paths around rectangular plots are becoming common among modern homeowners. In urban and suburban areas, this approach helps define zones within large yards, supports better movement, and improves drainage by elevating walking surfaces. The popularity reflects a shift toward organized, low-maintenance landscapes that prioritize both form and function—aligning with broader trends toward mindful home design and increased use of mobile devices to research DIY gardening solutions.", "How It Actually Works: The Mathematics Behind the Path", "The original garden measures 30 meters long and 20 meters wide. Without the path, its area is simply:", "\[ 30 \ imes 20 = 600 \ ext{ square meters} \]", "Adding a path uniformly surrounds this rectangle with a width \( x \)—meaning the path extends \( x \) meters on all sides. The total dimensions then become:", "- Length: \( 30 + 2x \) meters (adding \( x \) meters to each end) \n- Width: \( 20 + 2x \) meters", "The total area including the path is:", "\[\n(30 + 2x)(20 + 2x) = 1,000\n\]", "Expanding the equation:", "\[\n600 + 60x + 40x + 4x^2 = 1,000\n\]\n\[\n4x^2 + 100x + 600 = 1,000\n\]\n\[\n4x^2 + 100x - 400 = 0\n\]", "Dividing the"]