A rectangular garden is to be fenced on three sides, with a river forming the fourth side. The total cost of fencing is $480, and the fencing material costs $10 per linear foot. If the length of the garden parallel to the river is twice the width, what are the dimensions of the garden?

Wed, 29 Apr 2026 19:07:50 +0000

A rectangular garden fenced on three sides with a river forming the fourth side is a common solution driven by both practical land use and rising interest in sustainable living. This setup reduces material costs by leveraging natural boundaries, making it a popular choice for backyard growers and eco-conscious homeowners. With fencing priced at $10 per linear foot and a total budget of $480, the project’s math is straightforward—requiring 48 linear feet of fencing. Paired with a geometric relationship where the garden’s length runs parallel to the river and is twice the width, the dimensions reveal a balance between cost efficiency and functional design. The answer unfolds neatly, offering not just numbers, but clarity for real-world planning. Why a Fencing Strategy with River Boundaries Is Trending
This type of garden design resonates with current U.S. homeowner trends: maximizing outdoor space with minimal investment, enhancing property value through outdoor living areas, and integrating smart water management. The river side eliminates fencing costs entirely, redirecting effort to only three sides—typically two widths and one length. This efficiency resonates in a market where budget mindfulness meets outdoor lifestyle expansion, especially as more families prioritize weekend retreats and sustainability. Social media discussions and home improvement forums highlight growing curiosity about how to calculate optimal layouts, making this topic highly searchable and relevant for those planning garden projects. How the Math Comes Together
With $480 allocated at $10 per linear foot, the required fencing length is precisely 48 linear feet. Let the width across the river be \( w \), then the parallel length—twice the width—is \( 2w \). Since only three sides need fencing, the total fencing used equals \( w + 2w + w = 4w \). Setting \( 4w = 48 \), solving gives \( w = 12 \) feet, so the length is \( 24 \) feet. This clean breakdown shows how budget limits and dimensional relationships create a lean, practical design. The numbers offer a model for budgeting and space planning, vital for real-world application. Common Questions About the Garden Dimensions
Many users ask: how do I calculate dimensions when fencing cost and garden ratio are known? First, confirm total cost divided by price per foot to find material length. Then use width and length ratio—length = 2 × width—to form a simple equation. Also, remember total linear feet equals sum of the three sides: one width, two lengths. Clarifying roles—like the river as a free boundary—affects placement and math. These steps help readers replicate the solution effortlessly, making the project accessible for all skill levels.