A rectangular garden has a length that is 3 times its width. If the perimeter is 64 m, find the dimensions of the garden.
["### How to Find the Dimensions of a Rectangular Garden When Perimeter and Length-to-Breadth Relationship Are Known", "When designing or measuring a rectangular garden, understanding the relationship between its length, width, and perimeter is key. Imagine a garden where the length is exactly three times its width, and the total perimeter measures 64 meters. This classic scenario is a popular example in algebra and geometry, helping beginners and homeowners alike uncover the garden’s true dimensions.", "#### Understanding the Relationship", "In any rectangle, the perimeter is calculated using the formula:", "[\nP = 2 \ imes (\ ext{Length} + \ ext{Width})\n]", "Here, the length ( L ) is three times the width ( W ), so we write:", "[\nL = 3W\n]", "#### Setting Up the Equation", "Substitute ( L = 3W ) into the perimeter formula:", "[\n64 = 2 \ imes (3W + W)\n]", "Simplify inside the parentheses:", "[\n64 = 2 \ imes 4W\n]\n[\n64 = 8W\n]", "#### Solving for Width", "Divide both sides by 8:", "[\nW = \frac{64}{8} = 8 \ ext{ meters}\n]", "#### Finding the Length", "Now multiply to find the length:", "[\nL = 3W = 3 \ imes 8 = 24 \ ext{ meters}\n]", "#### Final Dimensions", "Thus, the rectangular garden measures:", "- Width: 8 meters\n- Length: 24 meters", "Check the perimeter:", "[\n2 \ imes (24 + 8) = 2 \ imes 32 = 64 \ ext{ meters}\n]", "This confirms the solution is accurate.", "#### Why This Matters", "Knowing how to calculate garden dimensions is valuable for planning space, estimating fencing costs, laying out borders, or planting designs. When a rectangle’s length is a multiple of its width—such as 3:1—solving perimeter problems becomes straightforward with basic algebra.", "---", "By applying simple equations, you can quickly determine the size of any rectangular garden, no matter its scale. So next time you encounter a similar problem, remember: length three times width and perimeter 64 m leads right to 8 m × 24 m.", "Keywords: rectangular garden dimensions, length 3 times width, perimeter calculation, garden design algebra, solve garden size, perimeter problem solved", "Meta Description: Discover how to find the width and length of a rectangular garden with a 3:1 length-to-width ratio and a 64 m perimeter using basic algebra and perimeter formulas."]
