A rectangular garden has a length that is 3 meters more than twice its width. If the perimeter is 54 meters, find the dimensions.
["How to Calculate the Dimensions of a Rectangular Garden with a Given Perimeter", "Understanding the dimensions of a rectangular garden based on its perimeter is a practical application of algebra that helps gardeners and homeowners plan space efficiently. In this article, we’ll solve a real-world problem: finding the length and width of a rectangular garden when the perimeter is known and a relationship exists between the length and width.", "---", "### Problem Statement", "We are given two key pieces of information:", "1. The length (L) of the rectangular garden is 3 meters more than twice its width (W).\n This relationship can be written algebraically as:\n [\n L = 2W + 3\n ]", "2. The perimeter of the garden is 54 meters.\n For a rectangle, the perimeter ( P ) is calculated by:\n [\n P = 2(L + W)\n ]\n Substituting the given value:\n [\n 2(L + W) = 54\n ]", "---", "### Step-by-Step Solution", "Step 1: Simplify the perimeter equation.", "[\n2(L + W) = 54\n]", "Divide both sides by 2:\n[\nL + W = 27\n]", "Step 2: Substitute the expression for ( L ) from the first equation.", "[\n(2W + 3) + W = 27\n]", "Step 3: Combine like terms.", "[\n3W + 3 = 27\n]", "Step 4: Solve for ( W ).", "[\n3W = 27 - 3 = 24\n]\n[\nW = \frac{24}{3} = 8 \ ext{ meters}\n]", "Step 5: Use the value of ( W ) to find ( L ).", "[\nL = 2W + 3 = 2(8) + 3 = 16 + 3 = 19 \ ext{ meters}\n]", "---", "### Final Answer", "The dimensions of the garden are:\n- Width = 8 meters\n- Length = 19 meters", "---", "### Why This Matters", "Calculating garden dimensions using algebraic equations ensures accuracy in space planning, especially when adherence to perimeter constraints is critical. Whether designing a vegetable patch, flower bed, or landscaping project, knowing how to solve such problems empowers better decision-making for both layout and resource allocation.", "---", "Summary:\nGiven a rectangular garden with a perimeter of 54 meters and a length defined as “3 meters more than twice its width,” solving the system of equations reveals the width to be 8 meters and the length 19 meters. This method combines algebra with practical application—perfect for any garden designer or DIY enthusiast.", "---", "Keywords: rectangular garden dimensions, perimeter calculation, algebra in gardening, find length and width, garden planning tips, solve rectangular garden problem"]
