A rectangle's length is twice its width. If the perimeter is 60 meters, what is the area?
["### Unlocking the Secrets of Geometry: A Rectangle’s Dimensions & Area When Length is Twice the Width (Perimeter 60 m)", "Geometry surrounds us—from architectural blueprints to everyday objects—and understanding basic shapes like rectangles is both practical and foundational. If you’ve ever wondered how to calculate the area of a rectangle when the length is twice the width and the perimeter is exactly 60 meters, this guide is for you. Let’s dive into the math and real-world application.", "---", "### Understanding the Rectangle Relationship", "Given:\n- The length (L) of the rectangle is twice the width (W) → ( L = 2W )\n- The perimeter (P) is 60 meters → ( P = 60 , \ ext{m} )", "For any rectangle, the perimeter formula is:\n[\nP = 2(L + W)\n]", "Substitute ( L = 2W ) into the formula:\n[\n60 = 2(2W + W) = 2(3W) = 6W\n]", "Solving for ( W ):\n[\nW = \frac{60}{6} = 10 , \ ext{meters}\n]", "Now find the length:\n[\nL = 2W = 2 \ imes 10 = 20 , \ ext{meters}\n]", "---", "### Calculating the Area: A Simple Formula", "The area ( A ) of a rectangle is:\n[\nA = L \ imes W\n]", "Substitute the known values:\n[\nA = 20 , \ ext{m} \ imes 10 , \ ext{m} = 200 , \ ext{m}^2\n]", "---", "### Why This Matters", "Understanding how to calculate area using proportional relationships helps in numerous real-life scenarios:", "- Interior design: Estimating floor space\n- Gardening: Planning rectangular plots\n- Construction: Measuring materials for flooring or wall coverings\n- Education: Building foundational math skills", "---", "### Summary", "- Width (W): 10 meters\n- Length (L): 20 meters\n- Perimeter: 60 meters (matches given condition)\n- Area: 200 square meters", "By applying the simple property that length is twice the width and using the perimeter formula, we efficiently solve rectangle problems involving ratios—and achieve accurate area calculations every time.", "---", "Want more geometry insights? Explore how changing dimensions affects shape properties or learn about irregular polygons. Mastering these basics opens doors to advanced math and daily problem-solving!"]
