A rectangular garden measures 50 meters by 30 meters. If a path of uniform width is constructed inside the garden along its perimeter, reducing the area available for planting by 300 square meters, what is the width of the path? - Treasure Valley Movers
A rectangular garden measures 50 meters by 30 meters. If a path of uniform width is constructed inside the garden along its perimeter, reducing the area available for planting by 300 square meters, what is the width of the path?
A rectangular garden measures 50 meters by 30 meters. If a path of uniform width is constructed inside the garden along its perimeter, reducing the area available for planting by 300 square meters, what is the width of the path?
Planning a tranquil outdoor space often means balancing beauty with practicality—and for gardeners using rectangular plots, a common question arises: how does a uniform walkway along the perimeter affect planting area? With growing interest in sustainable home design and smart landscaping, homeowners are seeking precision in reducing lost garden space while maintaining walkability. This challenge is especially relevant now, as compact urban plots demand smarter use of every square meter.
Why This Question Resonates Across the U.S.
Across suburban and urban neighborhoods nationwide, small-scale gardeners face similar constraints: irregularly shaped plots with limited room for growth. Reducing usable planting space by 300 square meters while keeping walking paths uniform speaks to a broader trend of optimizing space in tightly budgeted, land-scarce environments. Mobile users increasingly seek clear, data-driven answers to manage outdoor investments thoughtfully—driving natural curiosity about dimensions, geometry, and impact.
Understanding the Context
The Math Behind the Walkway
Imagine a rectangular garden of 50m by 30m—totaling 1,500 square meters of land. Adding a path of uniform width x around the inside perimeter cuts out inner planting zones. The remaining planting area is determined by reducing both length and width by twice x (since the path borders all sides).
New planting dimensions:
Length = 50 – 2x
Width = 30 – 2x
New planting area:
(50 – 2x)(30 – 2x) = 1,500 – 300 = 1,200 square meters
Setting up the equation:
(50 – 2x)(30 – 2x) = 1,200
Key Insights
Expanding:
1500 – 100x – 60x + 4x² = 1,200
4x² – 160x + 1,500 = 1,200
4x² – 160x + 300 = 0
Dividing through by 4:
x² – 40x + 75 = 0
