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 1,800 square meters. What is the width of the path? - Sterling Industries
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 1,800 square meters. What is the width of the path?
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 1,800 square meters. What is the width of the path?
Curious homeowners, city planners, and property investors are increasingly puzzling over how expands rectangle-based outdoor spaces with surrounding walkways. This question isn’t just about math—it reflects a growing interest in smart land use and sustainable design. With rising demand for private green zones and outdoor living, understanding how uniform paths affect total area offers valuable insight into residential planning and property optimization.
Why This Problem Is Gaining Traction in the US
Understanding the Context
In recent years, American interest in functional outdoor spaces has surged. From backyard retreats to meditation gardens, the shift toward blending nature with private land use highlights a desire for peaceful, intentional environments. Expanding a rectangular plot—measuring 50 meters by 30 meters—with a uniform path reveals how simple geometry influences usable space. Due to increasing urban densification and rising property values, homeowners seek precise measurements to maximize value without over-extending land. This practical math challenge connects curiosity with real-world planning needs, making it popular across mobile searches focused on home development.
How Does a Uniform Path Enlarge Total Area?
The plot’s original dimensions are 50 meters long and 30 meters wide. Adding a path of uniform width (x) meters surrounds the entire rectangle. The new outer dimensions become:
- Length: (50 + 2x)
- Width: (30 + 2x)
Key Insights
The area of a rectangle is length multiplied by width, so the total area becomes:
[(50 + 2x)(30 + 2x) = 1,800]
Expanding this:
[(50 + 2x)(30 + 2x) = 1,500 + 100x + 60x + 4x^2 = 1,800]
Simplifying:
[4x^2 + 160x + 1,500 = 1,800]
[4x^2 + 160x - 300 = 0]
Dividing everything by 4 to simplify:
[x^
