A rectangular garden is 3 times as long as it is wide. If the perimeter is 64 meters, what is the area?
["Title: How to Calculate the Area of a Rectangular Garden with Given Perimeter and Length-to-Width Ratio", "When designing a rectangular garden, understanding the relationship between its dimensions and perimeter is essential — especially for efficient planning, landscaping, or budgeting. In this article, we’ll explore a classic geometry problem involving a rectangular garden that is 3 times as long as it is wide, with a perimeter of 64 meters, and we’ll calculate its exact area.", "---", "### Understanding the Problem", "We know two key facts:", "1. The garden is rectangular — it has a well-defined length and width.\n2. The length is 3 times the width.\n3. The perimeter is 64 meters.", "We are asked to find the area of the garden, which is calculated using the formula:", "> Area = Length × Width", "But first, we need to determine the exact values of the length and width using the perimeter.", "---", "### Step-by-Step Calculation", "Let’s define the variables:", "- Let the width = ( w ) meters\n- Then the length = ( 3w ) meters (since it’s 3 times the width)", "The perimeter (P) of a rectangle is given by the formula:", "[\nP = 2(\ ext{Length} + \ ext{Width})\n]", "Substituting the known values:", "[\n64 = 2(3w + w)\n]", "Simplify inside the parentheses:", "[\n64 = 2(4w)\n]\n[\n64 = 8w\n]", "Now, solve for ( w ):", "[\nw = \frac{64}{8} = 8 \ ext{ meters}\n]", "Now calculate the length:", "[\n\ ext{Length} = 3w = 3 \ imes 8 = 24 \ ext{ meters}\n]", "---", "### Calculate the Area", "Now that we have:", "- Width = 8 m\n- Length = 24 m", "Area = Length × Width:", "[\n\ ext{Area} = 24 \ imes 8 = 192 \ ext{ square meters}\n]", "---", "### Final Answer", "The area of the rectangular garden is 192 m². This means the entire space available for planting, walking paths, or garden beds spans 192 square meters, offering plenty of room even within a moderately sized backyard.", "---", "### Why This Calculation Matters", "Knowing the area helps gardeners:", "- Determine how many plants or flowers can fit\n- Plan irrigation and watering systems\n- Estimate soil and fertilizer needs\n- Optimize space in small gardens or homeply spaces", "Using the relationship between perimeter, length, width, and area turns abstract garden design into precise, actionable planning.", "---", "Keywords for SEO: rectangular garden area calculation, rectangular garden dimensions, how to find garden area, perimeter to area formula, garden perimeter 64 meters, garden layout math, math problem garden, rectangle area with ratio, solve rectangular garden problem", "---", "By applying basic algebra and geometry, even simple garden shapes become powerful tools for smart landscaping. Whether you’re a homeowner, gardener, or student, understanding these principles helps turn a plot of land into a beautifully functional space."]
