A rectangular garden has a length of 15 meters and a width of 10 meters. A path of uniform width is built around it, increasing the total area to 286 square meters. What is the width of the path?

Wed, 06 May 2026 12:50:13 +0000

**Your Mobile-First Guide to Solving the Rectangular Garden Path Puzzle** **Why This Garden Math Problem Is Gaining Traction Online**
In an era where backyard spaces matter more than ever, homeowners and gardening enthusiasts are turning to simple spatial challenges like this rectangular garden with a 15m by 10m footprint. With rising interest in outdoor living and smart yard design, questions about area optimization—such as how a uniform path affects total space—are emerging across US digestive feeds and mobile search. This isn’t just a math problem; it’s a practical puzzle reflecting real-life asymmetries in garden planning and design. Curious users are seeking clarity, affirming that even small curves and corners can hide surprisingly precise geometric truths. **Why This Garden Layout Is More Than Just Dimensions**
A rectangular garden measuring 15 meters in length and 10 meters in width feels straightforward—but adding a surrounding path of uniform width transforms basic geometry into a manageable real-world application. With a total enclosed area of 286 square meters, users seek the precise dimension of the path that symmetrically encloses the garden without altering its core shape. This type of inquiry reflects growing awareness of how outdoor infrastructure influences value, usability, and aesthetics—key factors in smart home decision-making across the US. **How the Path Expands the Total Area to 286 Square Meters**
Let’s break it down simply: the garden is fixed at 15m (length) by 10m (width), giving an initial area of 150 square meters. With a uniform path of width *x* meters surrounding it, the total length and width grow:
- New length: 15 + 2x
- New width: 10 + 2x
Multiplying these gives the total area:
(15 + 2x)(10 + 2x) = 286
Expanding and solving this quadratic equation reveals the actual width: *x* = 2 meters. This appealing result proves that even small uniform expansions can dramatically increase usable outdoor space—making the math instantly relevant to modern yard optimization.