A rectangular garden is 15 meters long and 10 meters wide. A path of uniform width is laid around the garden, increasing the total area to 286 square meters. What is the width of the path? - Deep Underground Poetry
A rectangular garden is 15 meters long and 10 meters wide. A path of uniform width surrounds it, expanding the overall area to 286 square meters. What is the width of this path?
This question is gaining quiet traction across US home improvement and sustainable living communities. More homeowners and gardeners are integrating outdoor spaces into holistic yard planning—balancing function, sustainability, and aesthetics. As urban yards become denser, thoughtful design with paved paths now plays a growing role—not just for mobility, but for defining usable space and enhancing property value.
A rectangular garden is 15 meters long and 10 meters wide. A path of uniform width surrounds it, expanding the overall area to 286 square meters. What is the width of this path?
This question is gaining quiet traction across US home improvement and sustainable living communities. More homeowners and gardeners are integrating outdoor spaces into holistic yard planning—balancing function, sustainability, and aesthetics. As urban yards become denser, thoughtful design with paved paths now plays a growing role—not just for mobility, but for defining usable space and enhancing property value.
A 15m × 10m garden measures 150 square meters. Adding a uniform path around the perimeter increases that footprint to 286 square meters, meaning extra area equals the path’s expanded border. Can you picture the math? The original garden sits centrally—path width defined on each side. Calculating this reveals how subtle dimensional changes impact space dramatically.
To solve, imagine the path adds x meters evenly to each side. The new total dimension becomes (15 + 2x) meters long and (10 + 2x) meters wide.
Area equation: (15 + 2x)(10 + 2x) = 286
Expanding: 150 + 30x + 20x + 4x² = 286 → 4x² + 50x + 150 = 286
Simplifying: 4x² + 50x – 136 = 0
Divide by 2: 2x² + 25x – 68 = 0
Understanding the Context
Use the quadratic formula: x = [–25 ± √(625 + 544)] / 4 = [–25 ± √1169] / 4
√1169 ≈ 34.2 → x ≈ (–25 + 34.2) / 4 ≈ 9.2 / 4 ≈ 2.3 meters
The uniform path width is approximately 2.3 meters. Dividing the total added area by perimeter expansion confirms precision. This approach balances formulaic rigor with practical calculation—ideal for users drawn to data-driven solutions.
Why might this calculation matter now? Rising interest in outdoor living, sustainable landscaping, and smart home integration fuels demand for accurate design tools. People seek clarity: is a wider path necessary, or can a moderate width suffice? This problem reflects broader trends—owners weigh cost, space, and durability when shaping their front yards or back gardens.
Many users wonder: Is this path truly worthwhile? Benefits include extended usability—wider walkway, better drainage, and defined edges that prevent soil erosion. Since the garden stays compact but gains usable area through thoughtful extension, a 2.3-meter path often strikes a balance
