A rectangular garden has a length that is 3 times its width. If the perimeter is 64 meters, what is the area of the garden?
["How to Calculate the Area of a Rectangular Garden: A Step-by-Step Guide", "If you’ve ever wondered how to find the area of a rectangular garden using its dimensions and perimeter, you’re in the right place. In this article, we’ll explore a classic geometry problem: a rectangular garden where the length is 3 times the width, and the perimeter is 64 meters. By following a simple calculation, we’ll uncover not only the perimeter details but also the exact area of the garden.", "### Understanding the Relationship Between Length and Width", "Let’s define the variables first:", "- Let the width of the garden be $ w $ meters.\n- Since the length is 3 times the width, the length $ l = 3w $.", "Modern gardens often use simple rectangular layouts for efficient planting and access, making such proportions common.", "### Using the Perimeter to Find Dimensions", "The perimeter $ P $ of a rectangle is given by the formula:\n$$ P = 2(\ ext{length} + \ ext{width}) = 2(l + w) $$", "We know the perimeter is 64 meters:\n$$ 2(3w + w) = 64 $$", "Simplify inside the parentheses:\n$$ 2(4w) = 64 $$\n$$ 8w = 64 $$", "Now, solve for $ w $:\n$$ w = \frac{64}{8} = 8 \ ext{ meters} $$", "Now find the length:\n$$ l = 3w = 3 \ imes 8 = 24 \ ext{ meters} $$", "### Calculate the Area of the Garden", "The area $ A $ of a rectangle is:\n$$ A = \ ext{length} \ imes \ ext{width} $$\n$$ A = 24 \ imes 8 = 192 \ ext{ square meters} $$", "### Final Answer", "The rectangular garden with a length 3 times its width and a perimeter of 64 meters has an area of 192 square meters.", "---", "### Why This Matters", "Knowing how to calculate garden areas helps both amateur gardeners and landscapers plan their space efficiently. By using algebraic relationships and perimeter formulas, even complex garden designs become manageable.", "Keywords: rectangular garden area, how to find area given perimeter, garden dimensions math, math problem solution, rectangle perimeter formula, garden layout calculation, width and length garden problem.", "Start your garden planning today—accurate measurements mean healthier plants and beautiful outdoor spaces!"]
