A rectangular garden measures 15 meters by 8 meters. If a walkway of uniform width is built around the garden, increasing the total area to 208 square meters, what is the width of the walkway? - Coaching Toolbox
A rectangular garden measures 15 meters by 8 meters. If a walkway of uniform width is built around the garden, increasing the total area to 208 square meters, what is the width of the walkway?
A rectangular garden measures 15 meters by 8 meters. If a walkway of uniform width is built around the garden, increasing the total area to 208 square meters, what is the width of the walkway?
As outdoor living spaces grow in popularity, homeowners increasingly explore ways to expand small gardens into inviting, functional areas—without losing the charm of their original layout. The classic 15 by 8 meter garden blends seamlessly into American suburban designs, offering a proven scale for backyard planning. Adding a thoughtfully designed walkway around such a garden transforms circulation and usability, turning the space into a more connected, inviting environment. Now, a simple math puzzle—what width creates a total area of 208 square meters? This question reflects growing interest in smart garden design solutions that enhance both beauty and function.
Why This Question Is Gaining Attention in the US
Understanding the Context
Current trends highlight a shift toward giving outdoor spaces purpose beyond decoration—extending living areas with comfort and safety in mind. With rising home values and a focus on sustainable living, many U.S. homeowners are reimagining tight yards, balancing greenery with walkability. The 15 by 8 meter garden, a common footprint found in countless American backyards, represents a relatable size for conversation. Adding a uniform-width walkway isn’t just an aesthetic upgrade—it’s a practical response to how people move through, enjoy, and protect their outdoor areas. The specific detail of a 208 square meter total area grounds the query in tangible, real-world measurement, connecting curiosity to actionable planning.
How to Calculate the Walkway Width Around a Rectangular Garden
Imagine the garden as a simple rectangle: 15 meters long and 8 meters wide. A walkway surrounds it evenly, increasing both length and width by the same amount—let this uniform width be x meters. The new total dimensions become (15 + 2x) meters in length and (8 + 2x) meters in width. The total area of the garden plus walkway is then:
(15 + 2x)(8 + 2x) = 208
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Key Insights
Expanding this:
15×8 = 120
15×2x = 30x
8×2x = 16x
2x×2x = 4x²
So the equation reads:
4x² + 46x + 120 = 208
Subtract 208 from both sides:
4x² + 46x – 88 = 0
Dividing every term by 2 simplifies:
2x² + 23x – 44 = 0
This quadratic equation reveals the precise x value when solved accurately. Using the quadratic formula, x emerges safely and logically—showcasing how mathematical thinking brings tangible results to everyday home projects.
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Common Questions About This Garden Walkway Problem
H3: Is this calculation feasible for real gardens?
Yes. Many homeowners pursue similar projects using precise measurements. The method applies universally to rectangular layouts and supports informed decision-making.
H3: How accurate does the solution need to be?
Accuracy is key for proper construction. The calculated width ensures
