A rectangular garden has a perimeter of 60 meters and a length 5 meters more than twice its width. Find the dimensions.
["### Finding the Dimensions of a Rectangular Garden with a 60-Meter Perimeter", "Creating a rectangular garden offers practical benefits for both beauty and function. Whether for planting vegetables, flowers, or designing a peaceful outdoor space, knowing the exact dimensions helps with planning, fencing, and planting layout. In this article, we’ll solve a classic geometry problem: determining the length and width of a rectangular garden when its perimeter is 60 meters and the length is 5 meters more than twice its width.", "---", "### Problem Statement", "We are given:", "- The perimeter of the garden is 60 meters.\n- The length ( L ) is 5 meters more than twice the width ( W ).\n- The formula for the perimeter ( P ) of a rectangle is:\n [\n P = 2(L + W)\n ]", "Our goal is to find the values of ( L ) (length) and ( W ) (width).", "---", "### Step-by-Step Solution", "Step 1: Write down the perimeter formula", "[\n2(L + W) = 60\n]", "Divide both sides by 2:", "[\nL + W = 30 \quad \ ext{(Equation 1)}\n]", "Step 2: Express length in terms of width", "We’re told that the length is 5 meters more than twice the width:", "[\nL = 2W + 5 \quad \ ext{(Equation 2)}\n]", "Step 3: Substitute Equation 2 into Equation 1", "Replace ( L ) in Equation 1:", "[\n(2W + 5) + W = 30\n]", "Step 4: Solve for ( W )", "Combine like terms:", "[\n3W + 5 = 30\n]", "Subtract 5 from both sides:", "[\n3W = 25\n]", "Divide by 3:", "[\nW = \frac{25}{3} \approx 8.33 \ ext{ meters}\n]", "Step 5: Find the length ( L )", "Use Equation 2:", "[\nL = 2W + 5 = 2\left(\frac{25}{3}\right) + 5 = \frac{50}{3} + 5 = \frac{50}{3} + \frac{15}{3} = \frac{65}{3} \approx 21.67 \ ext{ meters}\n]", "---", "### Final Answer", "The dimensions of the garden are:", "- Width: ( \frac{25}{3} ) meters (≈ 8.33 m)\n- Length: ( \frac{65}{3} ) meters (≈ 21.67 m)", "Verifying the perimeter:\n[\n2\left(\frac{25}{3} + \frac{65}{3}\right) = 2 \cdot \frac{90}{3} = 2 \cdot 30 = 60 \ ext{ meters}\n]\n✅ Confirmed.", "---", "### Tips for Garden Planning", "- Knowing exact dimensions helps in estimating fencing materials (60 m perimeter means 60 meters of fencing or edging).\n- This garden layout supports a balanced design and efficient use of space.\n- Adjust plants according to light and growing conditions, which can vary along width and length.", "---", "By applying basic algebraic steps to the perimeter formula and the linear relationship between length and width, we found the accurate dimensions for any gardener looking to design a scientifically proportioned rectangular garden.", "---", "Keywords: rectangular garden dimensions, perimeter 60 meters, length twice width + 5, solve garden shape, garden planning math, two-variable equation garden, geometric garden dimensions", "---", "Meta Description:\nSolve for the exact dimensions of a rectangular garden with a 60-meter perimeter and length 5 meters more than twice the width. Step-by-step solution included."]
