A rectangle has a length that is twice its width. If the perimeter of the rectangle is 60 units, what is its area?
["Rectangle Dimensions Problem: Find Area When Length is Twice the Width and Perimeter is 60 Units", "Understanding the relationship between a rectangle’s length, width, and perimeter is essential for solving a wide range of geometry problems. One classic example involves a rectangle where the length is twice the width. This common scenario helps students and math learners practice algebraic thinking and basic perimeter-area calculations. In this article, we’ll guide you step-by-step through a real-world problem: finding the area of a rectangle with a perimeter of 60 units, where the length is twice the width.", "---", "### Problem Overview", "We are told:\n- A rectangle has a length that is twice its width.\n- The perimeter of the rectangle is 60 units.\n- We are asked to find the area.", "This problem is ideal for mastering formulas and solving equations in a practical context.", "---", "### Step-by-Step Solution", "#### Step 1: Define Variables\nLet:\n- Width = ( w ) units\n- Length = ( 2w ) units (since it’s twice the width)", "#### Step 2: Use the Perimeter Formula\nThe perimeter ( P ) of a rectangle is calculated as:\n[\nP = 2(\ ext{Length} + \ ext{Width}) = 2(2w + w)\n]", "Substitute the given perimeter:\n[\n60 = 2(2w + w)\n]", "Simplify inside the parentheses:\n[\n60 = 2(3w)\n]", "Multiply:\n[\n60 = 6w\n]", "#### Step 3: Solve for Width\nDivide both sides by 6:\n[\nw = \frac{60}{6} = 10\n]", "So, the width is 10 units.", "#### Step 4: Calculate Length\nSince length is twice the width:\n[\n\ ext{Length} = 2w = 2 \ imes 10 = 20 \ ext{ units}\n]", "#### Step 5: Find the Area\nThe area ( A ) of a rectangle is:\n[\nA = \ ext{Length} \ imes \ ext{Width} = 20 \ imes 10 = 200 \ ext{ square units}\n]", "---", "### Summary of Results", "- Width: 10 units\n- Length: 20 units\n- Perimeter: 60 units (matches given)\n- Area: 200 square units", "---", "### Why This Problem Matters", "Problems like this build foundational math skills by combining algebra with geometry. Understanding how perimeter influences dimensions helps in real-life applications such as construction, gardening, and design. Practicing problems where one side relates proportionally to the other (e.g., length = 2 × width) strengthens problem-solving confidence and algebraic reasoning.", "---", "### Key Takeaways", "- Always define variables clearly when solving geometry problems.\n- Use formulas consistently: perimeter ( P = 2(L + W) ), area ( A = L \ imes W ).\n- Substitution and solving linear equations are powerful tools in geometry.", "---", "### Final Note", "By following these simple steps, you can confidently solve similar rectangle problems — whether in homework, exams, or real-world planning. Remember: whether you’re calculating room dimensions or building a garden bed, the principles remain the same!", "---", "Keywords: rectangle perimeter and area, rectangle length twice width, solve rectangle with perimeter 60, geometry perimeter-area problem, algebra rectangle, width length relationship, calculating area from perimeter", "Meta Description: Learn how to find the area of a rectangle when the length is twice the width and the perimeter is 60 units. Step-by-step solution with formula breakdown."]
