A rectangle has a length that is 3 times its width. If the perimeter of the rectangle is 64 units, what is the area of the rectangle?
["Rectangle Perimeter & Area: Finding Area When Length is Three Times the Width", "Understanding the relationship between a rectangle’s length and width is essential in geometry. One common problem involves a rectangle where the length is three times the width and the perimeter is known. In this article, we’ll explore how to solve for the rectangle’s dimensions and calculate its area using real-world examples and math.", "---", "### Given:\n- The length of the rectangle ((L)) is 3 times the width ((W))\n- The perimeter is 64 units\n- Goal: Find the area of the rectangle", "---", "### Step 1: Set Up the Mathematical Relationships", "From geometry, the perimeter (P) of a rectangle is calculated using:\n[\nP = 2 \ imes (L + W)\n]", "We’re told (L = 3W) and (P = 64). Substitute (L) into the perimeter formula:\n[\n64 = 2 \ imes (3W + W)\n]", "Simplify inside the parentheses:\n[\n64 = 2 \ imes 4W\n]\n[\n64 = 8W\n]", "---", "### Step 2: Solve for the Width", "Divide both sides by 8:\n[\nW = \frac{64}{8} = 8\n]", "So, the width is 8 units.", "---", "### Step 3: Find the Length", "Since (L = 3W):\n[\nL = 3 \ imes 8 = 24\n]", "Thus, the length is 24 units.", "---", "### Step 4: Calculate the Area", "The area (A) of a rectangle is:\n[\nA = L \ imes W\n]\n[\nA = 24 \ imes 8 = 192\n]", "---", "### Final Answer:\nThe area of the rectangle is 192 square units.", "---", "### Why This Matters", "Knowing how to relate dimensions and use perimeter to find area is key in architecture, interior design, and manufacturing. Whether planning a garden bed, laying flooring, or designing a logo, understanding geometry helps ensure optimal use of space.", "Summary Checklist:\n- Given perimeter and ratio of length to width\n- Defined variables: (L = 3W), (P = 64)\n- Solved for (W = 8), (L = 24)\n- Area = 192 square units", "---", "### Key Takeaways\n- Use the perimeter formula (P = 2(L + W)) when dimensions are related.\n- Substitution simplifies problems involving ratios.\n- Area = length × width — a fundamental formula in geometry.", "For more geometry problems and calculations, explore our geometry section and master shapes with confidence!"]
