#### 11,6161. A rectangle has a length that is twice its width, and its perimeter is 48 units. What is the area of the rectangle?
["Solving Rectangle Problems: How to Find Area When Length is Twice the Width and Perimeter is Given", "If you’ve ever encountered a geometry problem like: “A rectangle has a length that is twice its width, and its perimeter is 48 units. What is the area of the rectangle?" — you’re in the right place. This classic problem helps reinforce key concepts used in algebra, geometry, and equation solving. In this article, we’ll walk through the step-by-step process to find the area, explain why the length being twice the width matters, and show how to apply perimeter and algebra to real-life scenarios.", "---", "### Understanding the Problem", "We are told:", "- The length (let’s call it L) is twice the width (W).\n → This gives us the equation:\n [\n L = 2W\n ]", "- The perimeter of the rectangle is 48 units.\n → The perimeter (P) of a rectangle is calculated by:\n [\n P = 2(L + W)\n ]\n So:\n [\n 2(L + W) = 48\n ]", "---", "### Step-by-Step Solution", "#### Step 1: Substitute Length in Perimeter Formula", "Start by substituting ( L = 2W ) into the perimeter equation:\n[\n2(2W + W) = 48\n]", "Simplify inside the parentheses:\n[\n2(3W) = 48\n]", "Multiply:\n[\n6W = 48\n]", "#### Step 2: Solve for Width", "Divide both sides by 6:\n[\nW = \frac{48}{6} = 8 \ ext{ units}\n]", "#### Step 3: Find Length", "Use the relationship ( L = 2W ):\n[\nL = 2 \ imes 8 = 16 \ ext{ units}\n]", "#### Step 4: Calculate the Area", "The area (A) of a rectangle is:\n[\nA = L \ imes W = 16 \ imes 8 = 128 \ ext{ square units}\n]", "---", "### Final Answer:\nThe area of the rectangle is 128 square units.", "---", "### Why This Problem Matters", "Understanding how to solve rectangle area problems with given perimeter and proportional relationships builds foundational skills in:", "- Translating word problems into algebraic equations\n- Applying formulas consistently\n- Checking reasonableness of results\n- Connecting geometry to algebra", "Whether you're a student studying math, a teacher preparing lessons, or someone solving real-world measurement challenges, knowing how to handle these types of problems enables better problem-solving and confidence in math.", "---", "### Double-Check Your Work", "To verify:", "- Width = 8, Length = 16 → Perimeter: ( 2(8+16) = 48 ) ✅\n- Length is twice width → ( 16 = 2 \ imes 8 ) ✅\n- Area: ( 16 \ imes 8 = 128 ) ✅", "---", "Try It Yourself:\nWhen you encounter similar problems, remember: define variables clearly, substitute relationships into formulas, solve systematically, and always check your work. The rectangle area problem with length twice the width is a perfect example of how geometry and algebra work together.", "---", "Keywords:\nrectangle area calculation, rectangle perimeter formula, solve for width and length, geometry problem, algebra and geometry, rectangle with length twice width, perimeter and area calculation, math problem solution", "Meta Description:\nLearn how to find the area of a rectangle where the length is twice the width and the perimeter is 48 units. Step-by-step solution with clear explanations and verification. Ideal for students and math learners."]
