A rectangular plot of land measures 50 meters by 30 meters. A path of uniform width is built around the plot, increasing the total area to 1,980 square meters. Find the width of the path. - Sterling Industries
Why a Simple Outdoor Path Can Change How You Use Your Land—And Why It Matters
Why a Simple Outdoor Path Can Change How You Use Your Land—And Why It Matters
Have you ever wondered how a quiet stretch of land transforms when a deliberate path draws the eye around it? The standard rectangular plot measuring 50 meters by 30 meters creates a familiar, functional space—but adding a uniform path around the edges dramatically alters its perceived and usable size. Now, imagining a 50x30 plot with a 2-meter-wide path around it yields a total area of 1,980 square meters—a detail that opens a conversation about smart outdoor design in the U.S.
This shift in area reflects more than a number. As urban landscapes grow tighter and suburban properties face rising demands for multifunctional space, attracting attention to compact, thoughtful layouts is increasingly relevant. A uniform path not only enhances aesthetics but also influences how we’ve come to describe space efficiency and outdoor investment in modern home planning.
Understanding the Context
A rectangular plot of land measures 50 meters by 30 meters. A path of uniform width is built around the plot, increasing the total area to 1,980 square meters. Find the width of the path.
Understanding how path width impacts total area begins with simple geometry. The original plot covers 1,500 square meters (50 × 30). Adding a path of uniform width w around it extends each dimension by 2w, resulting in new dimensions of (50 + 2w) by (30 + 2w). The expanded area follows this formula:
(50 + 2w)(30 + 2w) = 1,980
Expanding and simplifying, the equation becomes:
1,500 + 160w + 4w² = 1,980
4w² + 160w – 480 = 0
Dividing through by 4:
w² + 40w – 120 = 0
Key Insights
Using the quadratic formula,
w = [–40 ± √(1,600 + 480)] / 2
w = [–40 ± √2,080] / 2
w ≈ [–40 ± 45.6] / 2
Only the positive solution applies:
w ≈ (5.6) / 2 ≈ 2.8 meters
This calculation shows that a 2.8-meter-wide path doubles the usable visual footprint—demonstrating how
