A rectangle has a length that is twice its width. If the perimeter is 36 cm, find the dimensions of the rectangle.
["Rectangle Dimensions: How to Calculate Length and Width When Perimeter Is Given", "Understanding the relationship between a rectangle’s length, width, and perimeter is essential in geometry. In this article, we’ll explore how to find the dimensions of a rectangle where the length is twice the width, and the total perimeter is 36 cm. This straightforward problem is a great example of applying basic algebraic formulas and can help learners strengthen their math skills step by step.", "### What Is a Rectangle?\nA rectangle is defined by two measurements: length (L) and width (W). A key property is that the opposite sides are equal, and the perimeter (P) is calculated using the formula:", "[\nP = 2 \ imes (L + W)\n]", "### Given Conditions\n- The length (L) is twice the width:\n[\nL = 2W\n]\n- The perimeter (P) is 36 cm:\n[\nP = 36 \ ext{ cm}\n]", "### Finding the Dimensions Step-by-Step", "1. Substitute the relationship between L and W into the perimeter formula:\n[\n36 = 2 \ imes (2W + W)\n]", "2. Simplify the expression inside the parentheses:\n[\n36 = 2 \ imes 3W\n]\n[\n36 = 6W\n]", "3. Solve for width (W):\n[\nW = \frac{36}{6} = 6 \ ext{ cm}\n]", "4. Find the length (L) using ( L = 2W ):\n[\nL = 2 \ imes 6 = 12 \ ext{ cm}\n]", "### Final Answer\nThe rectangle has:\n- Width (W): 6 cm\n- Length (L): 12 cm", "### Repeatable Formula for Quick Validation\nFor any rectangle where length is twice the width and the perimeter is known, you can use:\n[\nW = \frac{P}{6} \quad \ ext{and} \quad L = 2W = \frac{2P}{6} = \frac{P}{3}\n]\nPlugging in ( P = 36 ):\n[\nW = \frac{36}{6} = 6 \ ext{ cm},\quad L = 2 \ imes 6 = 12 \ ext{ cm}\n]\nThis confirms our earlier result.", "### Why This Knowledge Matters\nUnderstanding how to calculate dimensions from a rectangle’s perimeter and side ratio builds foundational skills in algebra and geometry. It’s applied in real life—from framing rooms and packaging materials to designing digital layouts—making mastery of these steps valuable both in academics and everyday problem-solving.", "In summary: When dealing with a rectangle where the length equals twice the width and the perimeter is 36 cm, the width measures 6 cm and the length measures 12 cm. This clear, step-by-step breakdown simplifies complex problems and supports stronger STEM learning."]
