A rectangle's length is twice its width. If the perimeter is 48 cm, what are the rectangle's dimensions?
["How to Find a Rectangle’s Dimensions When Length Is Twice Its Width and the Perimeter Is 48 cm", "If you’re working with geometry problems involving rectangles, one common scenario is when the length of the rectangle is twice its width. Understanding how to translate this relationship into mathematical equations can help you solve for the exact dimensions efficiently. In this article, we’ll walk through a step-by-step solution to find the rectangle’s dimensions when its perimeter is 48 cm.", "---", "### Understanding the Relationship", "Given:\n- The length (L) is twice the width (W) → $ L = 2W $\n- The perimeter (P) is 48 cm → $ P = 48 $ cm", "A rectangle’s perimeter is calculated using the formula:\n$$ P = 2(L + W) $$", "---", "### Step-by-Step Solution", "Step 1: Substitute ( L = 2W ) into the perimeter formula.\n$$\n\begin{align}\nP &= 2(L + W) \\n48 &= 2(2W + W) \\n48 &= 2(3W) \\n48 &= 6W\n\end{align}\n$$", "Step 2: Solve for width (W).\n$$\nW = \frac{48}{6} = 8 \ ext{ cm}\n$$", "Step 3: Find the length using ( L = 2W ).\n$$\nL = 2 \ imes 8 = 16 \ ext{ cm}\n$$", "---", "### Final Answer", "The rectangle’s dimensions are:\n- Width: 8 cm\n- Length: 16 cm", "---", "### Why This Problem Matters", "Understanding how to model real-world relationships using algebraic equations is fundamental in geometry and engineering. Knowing how to use perimeter formulas with variable relationships helps in design, construction, and mapping tasks where precision is essential.", "If you're studying problems like this, practice transforming word-based relationships into mathematical expressions — it’s the key to solving many geometry puzzles quickly and accurately.", "---", "Keywords: rectangle dimensions, perimeter formula, length twice width, geometry problem solution, algebra in geometry, rectangle length vs width, how to find rectangle size, perimeter calculation, math problem steps."]
