A rectangular garden measures 30 feet by 40 feet. A path of uniform width is built around the garden, increasing the total area to 1,800 square feet. What is the width of the path? - inBeat
Why Common Garden Path Queries Are Surpassing Expectations in the U.S.
And How Expansive Layouts Are Shaping Modern Outdoor Spaces
Why Common Garden Path Queries Are Surpassing Expectations in the U.S.
And How Expansive Layouts Are Shaping Modern Outdoor Spaces
Curious homeowners, landscaping enthusiasts, and curious readers alike are increasingly exploring how simple garden designs can transform outdoor environments. A rectangular garden measuring 30 feet by 40 feet—about 1,200 square feet—often becomes the focal point when planners add a uniform path around it, amplifying both the footprint and aesthetic appeal. When combined with a significantly expanded total area of 1,800 square feet, users naturally ask: What width allows this geometry to harmonize efficiently? This exploration blends spatial math with practical outdoor planning, offering clarity for those looking to balance beauty, function, and scale.
Understanding the Context
What’s the Width of the Path When It Expands a 30x40 Feet Garden to 1,800 Square Feet?
The garden itself covers 1,200 square feet. Adding a uniform path along all sides increases this total to 1,800 square feet. To find the path width, consider the enclosure: each side adds twice the path width to the garden’s length and width. Mathematically, the total area including the path is given by:
$(30 + 2x)(40 + 2x) = 1800$
where $x$ is the path’s uniform width in feet.
Expanding this equation yields a quadratic:
$1200 + 140x + 4x^2 = 1800$
$4x^2 + 140x - 600 = 0$
Dividing through by 4:
$x^2 + 35x - 150 = 0$
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Key Insights
Solving this using the quadratic formula:
$x = \frac{-35 \pm \sqrt{35^2 + 4 \cdot 150}}{2} = \frac{-35 \pm \sqrt{1225 + 600}}{2} = \frac{-35 \pm \sqrt{1825}}{2}$
Approximately:
$x \approx \frac{-35 + 42.72}{2} = \frac{7.72}{2} = 3.
