A rectangle's length is twice its width, and its perimeter is 36 cm. What are the rectangle's dimensions?
["Rectangle Dimensions: How Length and Width Relate When Perimeter is 36 cm", "Understanding the relationship between a rectangle’s length, width, and perimeter is key to solving geometry problems efficiently. In this article, we break down what it means when a rectangle’s length is twice its width and its perimeter measures 36 cm. We’ll walk through the step-by-step process to find the exact dimensions—helping students, educators, and problem solvers alike.", "---", "### What Does It Mean When a Rectangle’s Length Is Twice Its Width?", "Let’s define the known variables:", "- Let the width of the rectangle = ( w ) cm\n- Since the length is twice the width, then ( \ ext{length} = 2w ) cm\n- The perimeter of a rectangle is calculated using the formula:\n [\n P = 2 \ imes (\ ext{length} + \ ext{width})\n ]", "---", "### Plugging in the Values", "Given that the perimeter ( P = 36 ) cm, substitute the expressions into the perimeter formula:", "[\n36 = 2 \ imes (2w + w)\n]", "Simplify inside the parentheses:", "[\n36 = 2 \ imes 3w = 6w\n]", "---", "### Solve for the Width", "Divide both sides by 6:", "[\nw = \frac{36}{6} = 6 \ ext{ cm}\n]", "Now, find the length:", "[\n\ ext{length} = 2w = 2 \ imes 6 = 12 \ ext{ cm}\n]", "---", "### Final Dimensions", "- Width: 6 cm\n- Length: 12 cm", "These dimensions satisfy both conditions:\n- Length is twice the width: ( 12 = 2 \ imes 6 )\n- Perimeter is 36 cm:\n [\n 2 \ imes (12 + 6) = 2 \ imes 18 = 36 \ ext{ cm}\n ]", "---", "### Why This Format Helps", "Presenting the relationship (“length = 2 × width”) visually and mathematically simplifies problem-solving. Recognizing such proportional relationships helps students quickly form equations and solve geometry problems with confidence.", "---", "### Summary", "For a rectangle where the length is twice the width and the perimeter is 36 cm, the width is 6 cm and the length is 12 cm. This classic geometry problem demonstrates how algebra and geometry combine to deliver clear, actionable answers—ideal for classroom learning and practical applications.", "---", "Key takeaway: In any rectangle, if length = twice the width and perimeter is known, define width as ( w ), express length as ( 2w ), plug into ( P = 2(l + w) ), and solve for dimensions efficiently.", "---", "Tags: rectangle dimensions, geometry problem, perimeter formula, length twice width, math solution, 36 cm perimeter, width and length, algebra geometry"]
