A rectangular garden has a length that is 3 meters longer than twice its width. If the perimeter is 54 meters, find the area of the garden.
["Calculating the Area of a Rectangular Garden with Algebra", "When designing a garden, precise measurements are essential to maximize space and ensure proper resource allocation. One common scenario involves rectangular garden plots with specific length and width relationships governed by algebraic expressions. This article explores how to determine the area of a rectangular garden given a precise linear relationship between its dimensions and a known perimeter.", "### Problem Setup", "We are told:\n- The length of a rectangular garden is 3 meters longer than twice its width.\n- The perimeter of the garden is 54 meters.\n- We need to find the area of the garden.", "Let’s define the variables:\nLet ( w ) represent the width of the garden in meters.\nThen, the length ( l ) can be expressed as:\n[\nl = 2w + 3\n]", "### Step 1: Use the Perimeter Formula", "The perimeter ( P ) of a rectangle is given by:\n[\nP = 2(l + w)\n]", "Substitute the known perimeter and the expression for ( l ):\n[\n54 = 2((2w + 3) + w)\n]", "Simplify inside the parentheses:\n[\n54 = 2(3w + 3)\n]", "Multiply through:\n[\n54 = 6w + 6\n]", "Subtract 6 from both sides:\n[\n48 = 6w\n]", "Divide by 6:\n[\nw = 8\n]", "### Step 2: Find the Length", "Now that we know ( w = 8 ), substitute into the length formula:\n[\nl = 2(8) + 3 = 16 + 3 = 19\n]", "So, the width is 8 meters, and the length is 19 meters.", "### Step 3: Calculate the Area", "The area ( A ) of a rectangle is:\n[\nA = l \ imes w = 19 \ imes 8 = 152\n]", "### Conclusion", "With a width of 8 meters and a length of 19 meters, the area of the rectangular garden is 152 square meters. This example demonstrates how algebraic reasoning—using relationships between dimensions and measurable parameters like perimeter—enables accurate garden planning and space utilization.", "By defining variables, forming equations from given conditions, and solving step-by-step, you can confidently calculate the area of any rectangular garden with similar constraints. Whether for landscaping, farming, or gardening enthusiasts, mastering such methods ensures both efficiency and clarity in design.", "---", "Keywords for SEO: rectangular garden area, garden perimeter calculation, solve garden dimensions algebraically, find rectangular garden area, garden design with equations, perimeter-based garden area, rectangular garden width and length, calculate garden area step by step, algebraic garden problem solution."]
