A rectangle has a length that is twice its width. If the perimeter of the rectangle is 36 meters, find the area of the rectangle.
["How to Calculate the Area of a Rectangle When Length is Twice the Width — Given a Perimeter of 36 Meters", "When learning geometry, understanding how to work with rectangles is essential — especially when relationships between dimensions and measurements such as perimeter and area are involved. One common problem involves a rectangle where the length is twice the width, and the perimeter is given. In this article, we’ll explore how to solve for the dimensions and find the area of such a rectangle with a perimeter of 36 meters.", "---", "### Understanding the Problem", "We are told:", "- The length ((L)) of the rectangle is twice its width ((W)):\n [\n L = 2W\n ]", "- The perimeter ((P)) is 36 meters.\n The formula for the perimeter of a rectangle is:\n [\n P = 2L + 2W\n ]", "Our goal is to find the area ((A)) of the rectangle, which is calculated as:\n[\nA = L \ imes W\n]", "---", "### Step-by-Step Solution", "Step 1: Express everything in terms of width\nSince (L = 2W), substitute this into the perimeter formula:\n[\nP = 2(2W) + 2W = 4W + 2W = 6W\n]", "We know (P = 36), so:\n[\n6W = 36\n]", "Step 2: Solve for width\n[\nW = \frac{36}{6} = 6 \ ext{ meters}\n]", "Step 3: Find the length\nUsing (L = 2W):\n[\nL = 2 \ imes 6 = 12 \ ext{ meters}\n]", "Step 4: Calculate the area\n[\nA = L \ imes W = 12 \ imes 6 = 72 \ ext{ square meters}\n]", "---", "### Key Takeaways", "- When a rectangle’s length is twice its width and the perimeter is known, expressing the dimensions in terms of a single variable simplifies the problem.\n- The area can then be easily computed using the formula (A = L \ imes W).\n- This method applies to a wide range of similar problems involving rectangles with proportional sides.", "---", "### Final Answer", "- Width: 6 meters\n- Length: 12 meters\n- Area: 72 square meters", "Using the perimeter of 36 meters and the condition that length is twice the width, we efficiently found that the rectangle’s area is 72 m² — a practical skill for students, architects, or DIY enthusiasts working with room layouts, building plans, or graphic design.", "---", "Keywords for SEO: rectangle area, perimeter and area, length twice width rectangle, solve rectangle problem, geometry tutorial, 36-meter perimeter rectangle, find area given proportions.", "---", "Start calculating your rectangle’s area today — perfect your geometric reasoning with clear, step-by-step formulas!"]
