A rectangular garden has a length that is 3 times its width. If the perimeter of the garden is 64 meters, what is the area of the garden in square meters?
["Rectangular Garden: Dimensions, Perimeter, and Area Calculations Explained", "Designing a rectangular garden can be both a fun and practical project—especially when you know precise measurements like length and width. Whether you're planning a flower bed, vegetable patch, or landscaping project, understanding how to calculate the area based on perimeter is essential. In this article, we’ll explore a classic gardening problem: a rectangular garden where the length is three times the width, and the perimeter is 64 meters. We’ll break down how to find the area in square meters, giving you both the mathematical process and practical insight.", "---", "### Understanding the Garden’s Dimensions", "Let’s start with the key facts:", "- The length (L) is 3 times the width (W):\n [\n L = 3W\n ]", "- The perimeter (P) of the rectangle is 64 meters.\n The formula for the perimeter of a rectangle is:\n [\n P = 2(L + W)\n ]", "Substitute ( L = 3W ) into the perimeter formula:", "[\n64 = 2(3W + W) = 2(4W) = 8W\n]", "Solve for ( W ):", "[\nW = \frac{64}{8} = 8 \ ext{ meters}\n]", "Now calculate the length:", "[\nL = 3W = 3 \ imes 8 = 24 \ ext{ meters}\n]", "---", "### Calculating the Area of the Garden", "The area (A) of a rectangle is given by:\n[\nA = L \ imes W\n]", "Substitute the known values:", "[\nA = 24 \ imes 8 = 192 \ ext{ square meters}\n]", "---", "### Final Thoughts", "Thus, a rectangular garden with a length three times its width and a perimeter of 64 meters has a total area of 192 square meters. This calculation ensures efficient use of space and helps gardeners determine planting capacity, soil needs, and maintenance planning. Understanding how perimeter and area relate through algebraic relationships empowers smarter design choices for any outdoor space.", "---", "Key takeaways:\n- Use the relationship ( L = 3W ) to express dimensions in terms of width.\n- Apply the perimeter formula to solve for width.\n- Multiply length and width to find area.\n- This method applies to a wide range of garden and landscaping projects.", "Start planning your rectangular garden with confidence—know its dimensions and area, and enjoy a beautiful, functional outdoor space!"]
