A rectangle has a length that is twice its width. If the perimeter is 60 meters, what is the area of the rectangle in square meters?
["Rectangle Dimensions: How Length Being Twice the Width Impacts Area", "Understanding the relationship between a rectangle’s length and width can simplify solving many geometry problems—especially when the perimeter is given. In this article, we’ll walk through a classic problem: identifying the dimensions of a rectangle where the length is twice the width, and the perimeter is 60 meters. We’ll also uncover how to calculate the area, expressed in square meters, giving both practical insight and a step-by-step explanation perfect for students, educators, and geometry enthusiasts.", "---", "### The Geometry Basics", "A rectangle has two dimensions: length and width. When the length is twice the width, we can express both measures algebraically. For clarity:", "- Let the width = ( w ) meters\n- Then, the length = ( 2w ) meters", "The perimeter ( P ) of a rectangle is calculated using the formula:\n[\nP = 2 \ imes (\ ext{length} + \ ext{width}) = 2 \ imes (2w + w) = 2 \ imes 3w = 6w\n]", "We’re told the perimeter is 60 meters, so:\n[\n6w = 60\n]", "---", "### Solving for Width and Length", "Divide both sides by 6:\n[\nw = 10 \ ext{ meters}\n]", "Since length is twice the width:\n[\n\ ext{length} = 2w = 2 \ imes 10 = 20 \ ext{ meters}\n]", "---", "### Calculating the Area", "The area ( A ) of a rectangle is given by:\n[\nA = \ ext{length} \ imes \ ext{width} = 20 \ imes 10 = 200 \ ext{ square meters}\n]", "---", "### Why This Problem Matters", "This simple problem exemplifies how algebraic relationships combined with geometric formulas help solve real-world design, architecture, and construction tasks. Knowing that a rectangle’s length being twice its width and knowing the perimeter allows for quick calculation of its area—essential for estimating materials, space planning, and site layout.", "---", "### Final Answer", "A rectangle with a length twice its width and a perimeter of 60 meters has an area of 200 square meters.", "---", "### Key Takeaways", "- Let width = ( w ), length = ( 2w )\n- Perimeter formula: ( 6w = 60 )\n- Solves to ( w = 10 ), length = 20\n- Area = ( 200 \ ext{ m}^2 )", "بإتقان فهمك لهذه العلاقات ستتمكن من التعامل مع العديد من المسائل الهندسية بشكل فعّال وسريع.", "---", "Keywords: rectangle area, perimeter formula, length twice width, rectangle dimensions, geometry problems, square meters area, algebraic geometry, perimeter and area relationship"]
