A rectangular garden has a length that is 3 meters more than twice its width. If the perimeter is 54 meters, find the width.
["How to Find the Width of a Rectangular Garden with a Given Perimeter", "When designing a rectangular garden, understanding the relationship between length, width, and perimeter is key. In this article, we’ll solve a common gardening math problem: finding the width of a rectangular garden where the length is 3 meters more than twice the width, and the total perimeter is 54 meters.", "---", "### Understanding the Problem", "We are told:", "- The garden is rectangular.\n- The length is 3 meters more than twice the width.\n- The perimeter is 54 meters.", "We need to find the width of the garden.", "---", "### Step-by-Step Solution", "Let’s define the variables first:", "- Let the width of the garden be ( w ) meters.\n- Then the length ( l ) is given as:\n [\n l = 2w + 3\n ]", "The perimeter ( P ) of a rectangle is calculated using the formula:\n[\nP = 2 \ imes (length + width)\n]", "Substitute the known values:\n[\n54 = 2 \ imes \left( (2w + 3) + w \right)\n]", "---", "### Simplify and solve the equation", "First, simplify inside the parentheses:\n[\n54 = 2 \ imes (3w + 3)\n]", "Now distribute the 2:\n[\n54 = 6w + 6\n]", "Subtract 6 from both sides:\n[\n48 = 6w\n]", "Divide both sides by 6:\n[\nw = 8\n]", "---", "### Final Answer", "The width of the rectangular garden is 8 meters.", "---", "### Bonus: Calculate the Length for Context", "Using ( w = 8 ):\n[\nl = 2(8) + 3 = 16 + 3 = 19 \ ext{ meters}\n]", "Check the perimeter:\n[\n2 \ imes (8 + 19) = 2 \ imes 27 = 54 \ ext{ meters} \quad \ ext{(Correct!)}\n]", "---", "### Why Knowing This Matters for Gardeners", "Accurately calculating dimensions helps with:", "- Estimating soil and mulch needs\n- Determining fencing requirements\n- Planning plant placement\n- Optimizing sunlight and water distribution", "Understanding the relationship between width, length, and perimeter empowers gardeners to design efficient and beautiful spaces.", "---", "### Key Takeaway", "Given a rectangular garden where length ( = 2 \ imes \ ext{width} + 3 ) and perimeter is 54 meters, solving the equation gives a width of 8 meters. Use this formula and method for any similar garden planning challenge.", "---", "Keywords: rectangular garden perimeter, find width rectangle, solve garden dimensions, perimeter formula, garden planning math, rectangular garden calculation, width and length relationship, recalculate garden size."]
