A rectangular garden is to be fenced, with the length being 3 times the width. If 64 meters of fencing is available, what is the maximum area of the garden?

Sun, 19 Apr 2026 16:16:10 +0000

**A rectangular garden is to be fenced, with the length being 3 times the width. If 64 meters of fencing is available, what is the maximum area of the garden?** In home design and outdoor planning, efficient use of space often centers on simple geometric principles—like designing a rectangular garden with a fixed perimeter to maximize planting area. This approach appeals to homeowners across the U.S. who are balancing aesthetics, usability, and sustainability with limited fencing materials. When the garden’s length is three times its width, and only 64 meters of fencing is available, understanding how to calculate the optimal dimensions unlocks smarter, cost-effective landscaping. This calculation isn’t just a classroom exercise—it’s increasingly relevant as families and gardeners seek practical, space-smart designs that thrive in real-world conditions. A rectangular garden fenced with length three times the width uses perimeter geometry to determine the best area possible. With exactly 64 meters of fencing, the perimeter formula—2(length + width)—becomes a strategic tool. Because length is 3 times width, substituting gives: perimeter = 2(3w + w) = 64 meters. This simplifies to 8w = 64, meaning the width is 8 meters and the length measures 24 meters. These dimensions reveal how a structured approach directly influences garden space, making it easier to plan gardens that accommodate both aesthetic appeal and functional use. The maximum area emerges cleanly from this math: width × length = 8 × 24 = 192 square meters. Far from coincidental, this result reflects the power of applying mathematical precision to outdoor projects. For millions of U.S. gardeners, this calculation underscores a fundamental truth—better planning leads to bigger, healthier gardens, reducing the need for costly redesigns or expansions later.