A rectangular garden has a length that is 4 meters longer than its width. If the perimeter is 40 meters, what is the area of the garden?

["Rectangular Garden: How to Calculate the Area When Dimensions Are Defined", "When designing a garden, understanding the relationship between length, width, and perimeter is essential for optimizing space and ensuring efficient layout. One classic problem involves a rectangular garden where the length exceeds the width by 4 meters, and the total perimeter is 40 meters. This article walks through the step-by-step solution and explains how to calculate the garden’s area, a key metric for gardening and landscaping planning.", "---", "### Understanding the Problem", "We are given:\n- The garden is rectangular.\n- The length is 4 meters longer than the width.\n- The perimeter of the garden is 40 meters.\n- We are to find the area of the garden.", "This classic algebraic word problem demonstrates how linear relationships and geometric formulas work together to provide practical answers in garden design and land use.", "---", "### Step-by-Step Solution", "#### Step 1: Define variables\nLet the width of the garden be ( w ) meters.\nThen, the length ( l ) is ( w + 4 ) meters, since it is 4 meters longer.", "#### Step 2: Use the perimeter formula for a rectangle\nThe perimeter ( P ) of a rectangle is given by:\n[\nP = 2 \ imes (length + width)\n]\nSubstitute the known values:\n[\n40 = 2 \ imes (w + (w + 4))\n]", "#### Step 3: Simplify and solve for ( w )\n[\n40 = 2 \ imes (2w + 4)\n]\n[\n40 = 4w + 8\n]\n[\n40 - 8 = 4w\n]\n[\n32 = 4w\n]\n[\nw = 8\n]", "#### Step 4: Calculate the length\nSince ( l = w + 4 ):\n[\nl = 8 + 4 = 12 \ ext{ meters}\n]", "#### Step 5: Calculate the area\nThe area ( A ) of a rectangle is:\n[\nA = length \ imes width = 12 \ imes 8 = 96 \ ext{ square meters}\n]", "---", "### Visual Summary", "| Measurement | Value (meters) |\n|-------------|----------------|\n| Width ((w)) | 8 |\n| Length ((l)) | 12 |\n| Perimeter | 40 (confirmed) |\n| Area | 96 |", "---", "### Why Knowing the Area Matters", "The area of the garden—96 square meters—is critical for planting decisions, soil preparation, and material estimation. Whether you’re planting vegetables, flowers, or laying down mulch, accurate area calculation ensures you use resources efficiently without waste.", "---", "### Practical Tips for Garden Planning", "- Always verify perimeter and area before purchasing plants or materials.\n- Consider irregular shapes or uneven spaces—this algebraic model works best with rectangular plots, but the principles scale.\n- Use graph paper or garden design software to visualize and adjust dimensions before finalizing.", "---", "### Conclusion", "A rectangular garden with a length 4 meters longer than its width and a perimeter of 40 meters has a total area of 96 square meters. By translating real-world garden dimensions into mathematical expressions for perimeter and area, you gain clarity and precision—key to successful gardening and landscape management. Whether you’re a beginner or experienced gardener, mastering these fundamentals helps you create productive, beautiful outdoor spaces.", "---", "Keywords: rectangular garden area, garden perimeter and area, how to calculate garden dimensions, rectangular garden math, garden planning formula, how large is a 40 meter perimeter garden, rectangular garden length width formula, garden area calculation."]