5Un rectángulo tiene una longitud que es el doble de su ancho. Si el perímetro del rectángulo es de 60 cm, ¿cuál es el área del rectángulo?
["How to Find the Area of a Rectangle When Perimeter and Side Ratio Are Given: A Step-by-Step Example", "If you're studying geometry or solving math problems, one common question involves rectangles with specific side relationships and a known perimeter. In this article, we’ll explore a typical problem: a rectangle where the length is twice the width and the perimeter is 60 cm, and discover how to calculate its area.", "---", "### Understanding the Rectangle’s Dimensions", "Let’s define the rectangle’s width as ( w ) cm. According to the problem, the length is twice the width, so:", "[\n\ ext{Length} = 2w\n]", "The perimeter ( P ) of a rectangle is calculated using the formula:", "[\nP = 2 \ imes (\ ext{Length} + \ ext{Width})\n]", "Substituting the known perimeter and expressions for length and width:", "[\n60 = 2 \ imes (2w + w)\n]", "Simplify inside the parentheses:", "[\n60 = 2 \ imes (3w)\n]", "[\n60 = 6w\n]", "Now, solve for ( w ):", "[\nw = \frac{60}{6} = 10 \ ext{ cm}\n]", "So, the width is 10 cm, and the length is:", "[\n2w = 2 \ imes 10 = 20 \ ext{ cm}\n]", "---", "### Calculating the Area", "The area ( A ) of a rectangle is:", "[\nA = \ ext{Length} \ imes \ ext{Width}\n]", "Substitute the values we found:", "[\nA = 20 \ imes 10 = 200 \ ext{ cm}^2\n]", "---", "### Final Answer", "When a rectangle has a length twice its width and a perimeter of 60 cm, its area is 200 square centimeters.", "---", "### Why This Problem Matters", "This type of question is common in geometry education because it teaches key concepts such as:", "- Relating length and width using ratios\n- Using perimeter formulas to find unknown dimensions\n- Calculating area from derived measurements", "Understanding how to break down a real-world geometric scenario into mathematical expressions helps build strong problem-solving skills in math.", "---", "Key Takeaway:\nGiven the relationship length = 2 × width and perimeter = 60 cm, solving step-by-step yields a width of 10 cm, length of 20 cm, and area of 200 cm².", "---", "Feel free to use this method anytime you encounter similar rectangle problems — whether in homework, exams, or practical applications!"]
