Question:** A rectangle has a length that is twice its width. If the perimeter is 36 units, what is the area of the rectangle?
["Finding the Area of a Rectangle: When Length is Twice the Width and Perimeter is 36 Units", "Understanding the relationship between a rectangle’s dimensions and its perimeter is a key concept in geometry. One common problem students and math enthusiasts encounter involves finding the area of a rectangle when the length is twice the width and the perimeter is known. In this article, we’ll walk through a classic example: a rectangle with a length twice its width and a perimeter of 36 units, and discover its area step by step.", "---", "### Understanding the Problem", "We’re given two important pieces of information:", "- The length ((L)) is twice the width ((W)):\n [\n L = 2W\n ]", "- The perimeter ((P)) is 36 units. The formula for the perimeter of a rectangle is:\n [\n P = 2L + 2W\n ]", "Our goal is to find the area of the rectangle, which is calculated as:\n[\n\ ext{Area} = L \ imes W\n]", "---", "### Step-by-Step Solution", "Step 1: Substitute length in the perimeter formula", "Start by substituting (L = 2W) into the perimeter equation:\n[\nP = 2L + 2W = 2(2W) + 2W = 4W + 2W = 6W\n]", "We know (P = 36), so:\n[\n6W = 36\n]", "Step 2: Solve for width (W)\n[\nW = \frac{36}{6} = 6 \ ext{ units}\n]", "Step 3: Find the length (L)\nSince (L = 2W):\n[\nL = 2 \ imes 6 = 12 \ ext{ units}\n]", "Step 4: Calculate the area\n[\n\ ext{Area} = L \ imes W = 12 \ imes 6 = 72 \ ext{ square units}\n]", "---", "### Final Result", "The rectangle has a width of 6 units, a length of 12 units, and an area of 72 square units when its perimeter is 36 units and the length is twice the width.", "---", "### Why This Problem Matters", "This type of problem helps build foundational algebraic skills by combining geometric formulas. It also demonstrates how variables and equations can model real-world relationships. Whether you’re preparing for exams or simply practicing problem-solving, mastering such problems improves logical thinking and mathematical fluency.", "---", "### Summary", "- Let width = (W), then length = (2W)\n- Perimeter = (2L + 2W = 6W)\n- Given perimeter = 36, solve for (W = 6)\n- Then (L = 12)\n- Area = (L \ imes W = 72) square units", "---", "Keywords: rectangle area, perimeter problem, twice the width rectangle, geometry exercise, solve rectangle dimensions, perimeter and area formula, algebra word problems", "Meta Description: Learn how to find the area of a rectangle when the length is twice the width and the perimeter is 36 units. Step-by-step solution with perimeter formulas and area calculation."]
