#### 121. A rectangle has a length that is twice its width. If the perimeter of the rectangle is 60 units, find the area of the rectangle.
["Solving Rectangle Problems: Finding the Area When Length is Twice the Width and Perimeter is 60 Units", "When tackling geometry problems, one of the most common and important types is finding the area of a rectangle given its perimeter and the relationship between its dimensions. A frequently asked question involves a rectangle where the length is twice the width, and the perimeter measures 60 units. Whether you're a student preparing for exams, a teacher explaining concepts, or someone learning geometry fundamentals, understanding how to solve this problem can strengthen your grasp of basic algebra and perimeter-area relationships.", "In this SEO-optimized guide, we’ll walk through step-by-step the process of finding the area of such a rectangle, emphasizing clear formulas, accurate calculations, and practical tips for solving similar rectangle problems.", "---", "### Understanding the Problem", "We are given:", "- The length (let's call it ( L )) is twice the width (let's call it ( W )):\n [\n L = 2W\n ]", "- The perimeter of the rectangle is 60 units:\n [\n \ ext{Perimeter} = 2(L + W) = 60\n ]", "Our goal is to find the area of the rectangle, defined as:\n[\n\ ext{Area} = L \ imes W\n]", "---", "### Step-by-Step Solution", "Step 1: Substitute Length in the Perimeter Formula", "Since ( L = 2W ), substitute this into the perimeter equation:", "[\n2(L + W) = 60\n]\n[\n2(2W + W) = 60\n]\n[\n2(3W) = 60\n]\n[\n6W = 60\n]", "Step 2: Solve for Width", "Divide both sides by 6:", "[\nW = \frac{60}{6} = 10 \ ext{ units}\n]", "Step 3: Find the Length", "Now use ( L = 2W ):", "[\nL = 2 \ imes 10 = 20 \ ext{ units}\n]", "Step 4: Calculate the Area", "Now compute the area:", "[\n\ ext{Area} = L \ imes W = 20 \ imes 10 = 200 \ ext{ square units}\n]", "---", "### Why This Problem Matters for SEO & Learning", "- This type of problem is optimized for keywords like “rectangle perimeter and area,” “solving rectangle dimensions,” “algebra geometry perimeter,” and “area from length and width.”\n- Including step-by-step explanations improves readability and user experience, key factors for SEO success.\n- Clear formulas and real-world application represent long-form content that search engines favor.", "---", "### Final Tips for Solving Similar Problems", "- Always express one dimension in terms of the other using the given ratio.\n- Substitute that expression into the perimeter or area formula.\n- Always check your units and calculations.\n- Use whole numbers when possible for simplicity and accuracy.\n- Practice with different ratios (e.g., 3:1, 4:1) to build confidence.", "---", "### Summary", "For a rectangle where the length is twice the width and the perimeter is 60 units, the width is 10 units, the length is 20 units, and the area is 200 square units. This classic geometry problem illustrates how relationships between dimensions translate into practical calculations—essential knowledge for anyone studying math basics.", "If you’re looking to master rectangle geometry, mastering these step-by-step methods and understanding underlying formulas will make learning both intuitive and effective. Begin with relationships like “length twice width,” and soon you’ll confidently solve similar problems every time.", "---", "Keywords: rectangle area, perimeter and area, length twice width, rectangle dimensions problem, geometry solved, algebra rectangle solutions, perimeter formula, find rectangle area, math problems 2024, geometry basics"]
