A rectangular garden has a length that is 4 meters more than its width. If the perimeter of the garden is 36 meters, what is the area of the garden?
["Rectangular Garden: Finding Area When Perimeter and Length-Width Relationship Are Defined", "If you're designing a rectangular garden and know key measurements, solving for the area becomes a straightforward yet rewarding exercise. One common scenario involves expressing the length and width in relation to each other—and using the perimeter to find exact dimensions. In this guide, we’ll explore a rectangular garden where the length is 4 meters more than its width, and the perimeter measures 36 meters. By applying basic algebra, we’ll uncover the garden’s area, enhancing your understanding of perimeter and area calculations in real-life landscaping.", "---", "### Understanding the Garden Dimensions", "Let’s define the variables first:", "- Let the width of the garden be ( w ) meters.\n- Then, the length is ( w + 4 ) meters, since it’s 4 meters longer than the width.", "The perimeter (P) of a rectangle is given by the formula:\n[\nP = 2 \ imes (\ ext{length} + \ ext{width})\n]\nSubstituting the known values:", "[\n36 = 2 \ imes (w + (w + 4))\n]", "---", "### Solving for the Width", "Start solving the equation step-by-step:", "1. Simplify inside the parentheses:\n[\n36 = 2 \ imes (2w + 4)\n]", "2. Multiply:\n[\n36 = 4w + 8\n]", "3. Subtract 8 from both sides:\n[\n28 = 4w\n]", "4. Divide both sides by 4:\n[\nw = 7\n]", "So, the width is 7 meters.", "---", "### Finding the Length", "Since the length is 4 meters more than the width:\n[\n\ ext{Length} = 7 + 4 = 11 \ ext{ meters}\n]", "---", "### Calculating the Area", "The area (A) of a rectangle is:\n[\nA = \ ext{length} \ imes \ ext{width}\n]\n[\nA = 11 \ imes 7 = 77 \ ext{ square meters}\n]", "---", "### Summary of Dimensions\n- Width: 7 meters\n- Length: 11 meters\n- Perimeter: 36 meters (as confirmed)\n- Area: 77 square meters", "---", "### Why This Matters", "Understanding how to calculate the area of a rectangular garden based on its perimeter and a fixed length-width relationship is valuable for planning space in landscaping, farming, or home gardening. Knowing these formulas helps optimize growth conditions, material needs, and overall efficiency.", "---", "In conclusion: For a rectangular garden where the length exceeds the width by 4 meters and the perimeter is 36 meters, the area is 77 square meters. This simple mathematical model illustrates how essential precision and algebra are in practical garden design.", "---", "Keywords: rectangular garden area, perimeter and width relationship, find garden area, solve garden dimensions algebraically, 36-meter perimeter garden, garden math, rectangular garden dimensions"]
