#### 2811. A rectangular garden has a length that is 3 times its width. If the perimeter of the garden is 64 meters, what is the width of the garden?
["Title: Solving the Equation: Finding the Width of a Rectangular Garden with Perimeter 64 Meters", "If you’re working with geometry or property landscaping, understanding how to calculate the dimensions of a rectangular garden is essential. One common scenario involves a rectangle where the length is three times the width and the perimeter is 64 meters. In this article, we’ll break down how to determine the width of such a garden step by step.", "---", "### Understanding the Problem", "We know from geometry that the perimeter (P) of a rectangle is given by the formula:\n[\nP = 2 \ imes (\ ext{length} + \ ext{width})\n]\nWe’re told:\n- The length ((L)) is 3 times the width ((W)), so (L = 3W)\n- The perimeter is 64 meters", "Substitute (L = 3W) into the perimeter formula:", "[\n64 = 2 \ imes (3W + W)\n]", "---", "### Step-by-Step Calculation", "1. Simplify the expression inside the parentheses:\n[\n64 = 2 \ imes (4W)\n]", "[\n64 = 8W\n]", "2. Solve for (W) by dividing both sides by 8:\n[\nW = \frac{64}{8} = 8\n]", "---", "### Final Answer", "The width of the garden is 8 meters. From this, the length is (3 \ imes 8 = 24) meters. You can verify this with the perimeter formula:\n[\n2 \ imes (24 + 8) = 2 \ imes 32 = 64 \ ext{ meters},\n]\nwhich matches the given perimeter.", "---", "### Why This Matters", "Recognizing this pattern helps in garden planning, fencing projects, and maximizing outdoor space efficiently. Knowledge of algebraic relationships between a rectangle’s dimensions simplifies real-life calculations, saving time and avoiding errors.", "---", "Key Takeaway:\nFor a rectangular garden with a perimeter of 64 meters and a length three times the width, the width is 8 meters. This straightforward equation-solving method applies broadly to similar geometry problems.", "---", "Keywords: rectangular garden, rectangle perimeter formula, solve for width, geometry problem solving, garden design, length three times width"]
