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 960 square meters. Find the width of the path. - Treasure Valley Movers
A rectangular garden with a length of 30 meters and width of 20 meters gains growing attention as people explore outdoor living spaces in the U.S. This popular design—simple yet highly adaptable—now inspires many homeowners looking to enhance functionality and curb appeal. When a uniform-width path surrounds such a garden, the overall footprint expands significantly. Intriguingly, this type of layout can increase the total area to as much as 960 square meters. The underlying question becoming common among curious homeowners is: what exactly is the width of this surrounding path? Understanding this calculation not only supports smart design choices but also reveals how subtle proportions affect real-world space. With a focus on clarity and practical insight, this article walks through the math and context—no technical jargon, no pressure, just essential knowledge.
A rectangular garden with a length of 30 meters and width of 20 meters gains growing attention as people explore outdoor living spaces in the U.S. This popular design—simple yet highly adaptable—now inspires many homeowners looking to enhance functionality and curb appeal. When a uniform-width path surrounds such a garden, the overall footprint expands significantly. Intriguingly, this type of layout can increase the total area to as much as 960 square meters. The underlying question becoming common among curious homeowners is: what exactly is the width of this surrounding path? Understanding this calculation not only supports smart design choices but also reveals how subtle proportions affect real-world space. With a focus on clarity and practical insight, this article walks through the math and context—no technical jargon, no pressure, just essential knowledge.
Why is a 30 by 20 meter garden with a surrounding path drawing attention now? The trend reflects rising demand for outdoor retreats amid urban lifestyle shifts and increased home improvement investment. Losing ground to concrete and screens, many Americans are redefining their backyards as sanctuaries for relaxation, small-scale gardening, or remote work. A uniform path adds both visual balance and usable hardscape space, merging nature with structure. The precise math behind the garden extension—calculating the path width from dimension changes—has become key guidance for these renovations. By uncovering how much space the path adds, homeowners gain confidence in planning larger, harmonious outdoor zones.
Let’s clarify the core question: A rectangular garden measuring 30 meters by 20 meters gains a uniform-width path around it, resulting in a total area of 960 square meters. What width should the path have?
Understanding the Context
To solve this, consider that the original garden spans 30 × 20 = 600 square meters. The path adds 960 − 600 = 360 square meters to that base footprint. The path surrounds the garden equally, so if the path width is x meters, the outer dimensions become (30 + 2x) meters by (20 + 2x) meters. The area of the full, reduced garden plus path is therefore (30 + 2x)(20 + 2x) = 960. Expanding this gives:
(30 + 2x)(20 + 2x) = 600 + 100x + 4x² = 960.
Subtracting 960 from both sides yields:
