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? - Treasure Valley Movers

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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.

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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:
$x^2 + 35x - 150 = 0$

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.