A rectangular garden has a length that is 3 meters more than twice its width. If the perimeter of the garden is 54 meters, what are the dimensions of the garden?
["Rectangular Garden Dimensions: Find Length and Width Using Perimeter and Length Relationship", "If you’ve ever wondered how to calculate the dimensions of a rectangular garden using only its perimeter and a mathematical relationship between its length and width, you’re in the right place. In this article, we’ll explore a practical problem: a rectangular garden where the length is 3 meters more than twice the width, and the perimeter is 54 meters. By applying basic algebra and perimeter formulas, we’ll uncover the exact dimensions that fit these conditions.", "---", "### Understanding the Problem", "We’re given two key pieces of information:", "1. The length ( L ) of the garden is related to the width ( W ) by:\n [\n L = 2W + 3\n ]\n2. The perimeter ( P ) of the rectangle is:\n [\n P = 2L + 2W = 54 \ ext{ meters}\n ]", "Our goal is to find the numerical values of ( L ) and ( W ) that satisfy both equations.", "---", "### Step-by-Step Solution", "Step 1: Substitute the length expression into the perimeter formula.\nUsing ( L = 2W + 3 ), plug this into the perimeter equation:", "[\n2L + 2W = 54\n]\n[\n2(2W + 3) + 2W = 54\n]", "Step 2: Expand and simplify.\nDistribute the 2:", "[\n4W + 6 + 2W = 54\n]", "Combine like terms:", "[\n6W + 6 = 54\n]", "Step 3: Solve for width ( W ).\nSubtract 6 from both sides:", "[\n6W = 48\n]", "Divide both sides by 6:", "[\nW = 8 \ ext{ meters}\n]", "Step 4: Find the length ( L ).\nUsing the earlier relationship:", "[\nL = 2W + 3 = 2(8) + 3 = 16 + 3 = 19 \ ext{ meters}\n]", "---", "### Final Garden Dimensions", "- Width: 8 meters\n- Length: 19 meters", "### Verification", "Let’s double-check the perimeter with these dimensions:", "[\n2L + 2W = 2(19) + 2(8) = 38 + 16 = 54 \ ext{ meters} \quad \ ext{✔}\n]", "And confirm the length relationship:", "[\nL = 2(8) + 3 = 19 \quad \ ext{✔}\n]", "Both conditions are satisfied, confirming our solution.", "---", "### Why Knowing Garden Dimensions Matters", "Understanding how to calculate a garden’s size using perimeter and internal ratios is useful for gardening, landscaping, and home improvement projects. Whether planning flower beds, vegetable plots, or fencing installations, accurate measurements prevent wasted materials and ensure a cohesive design.", "---", "### Summary", "| Parameter | Value |\n|----------------|----------------|\n| Width ( W ) | 8 meters |\n| Length ( L ) | 19 meters |\n| Perimeter ( P ) | 54 meters |\n| Length Formula | ( L = 2W + 3 ) |", "---", "### Key Takeaways", "- Use the perimeter formula ( P = 2L + 2W ) and substitute known relationships to solve for unknowns.\n- Always verify your solution by plugging values back into original conditions.\n- A rectangular garden with perimeter 54 meters and length 3 meters more than twice the width has dimensions 8 meters by 19 meters.", "---", "If you’re working on a gardening project or just exploring geometry, solving rectangle problems like this strengthens your mathematical skills and supports real-world planning. Now you know how to find the perfect garden shape—measure properly, calculate smartly!", "---", "Keywords: rectangular garden dimensions, find garden width and length, perimeter and length relationship, 54 meter garden, algebra garden problem, solve garden dimensions, garden geometry, math for landscaping."]
