A rectangle's length is 3 times its width. If the perimeter is 64 cm, what is the width of the rectangle?
["Title: How to Find the Width of a Rectangle When Length is 3 Times Its Width & Perimeter Is 64 cm", "When solving geometry problems involving rectangles, understanding the relationship between length, width, and perimeter is essential. In this article, we’ll walk through a common problem: a rectangle where the length is 3 times the width, and the perimeter is 64 cm. We’ll explain step-by-step how to calculate the width, making it easy for students, learners, and math enthusiasts to grasp the concept.", "---", "### Understanding the Rectangle Shape", "A rectangle is defined by two dimensions: length and width. One key relationship in rectangles is that the perimeter depends directly on both measurements:", "[\n\ ext{Perimeter} = 2 \ imes (\ ext{Length} + \ ext{Width})\n]", "We are told:", "- Length = 3 × Width\n- Perimeter = 64 cm", "Let’s define the width as a variable to simplify the formula.", "---", "### Step 1: Define Variables", "Let:", "- Width = ( w ) cm\n- Length = ( 3w ) cm (since length is 3 times the width)", "---", "### Step 2: Plug into the Perimeter Formula", "[\n\ ext{Perimeter} = 2 \ imes (\ ext{Length} + \ ext{Width}) = 2 \ imes (3w + w)\n]", "Simplify inside the parentheses:", "[\n2 \ imes (4w) = 64\n]", "---", "### Step 3: Solve for ( w )", "[\n8w = 64\n]", "Divide both sides by 8:", "[\nw = \frac{64}{8} = 8\n]", "---", "### Final Answer", "The width of the rectangle is 8 cm.", "---", "### Bonus: Calculate the Length", "Since length is 3 times the width:", "[\n\ ext{Length} = 3 \ imes 8 = 24 \ ext{ cm}\n]", "Verify the perimeter:", "[\n2 \ imes (24 + 8) = 2 \ imes 32 = 64 \ ext{ cm}\n]", "✅ Perfect match!", "---", "### Why This Problem Matters", "This type of problem strengthens foundational algebra and geometry skills. It teaches:", "- How to express variables based on word problems\n- The application of formulas in real-world contexts\n- Logical step-by-step problem solving", "Whether you're studying for exams, teaching math, or exploring geometry, understanding how to break down statements into equations is invaluable.", "---", "Key Terms for SEO:\nrectangle perimeter, rectangle dimensions, length is 3 times width, solve rectangle width, geometry problems with perimeter, algebra for kids, how to find rectangle dimensions", "Meta Description:\nLearn how to find the width of a rectangle when the length is 3 times the width and the perimeter is 64 cm. Step-by-step explanation with formula and verification.", "Keywords: rectangle width, perimeter calculation, length 3x width, solve geometry problem, rectangle formula", "---", "If you found this guide helpful, share it with fellow learners and explore more geometry tutorials to build confidence in math!"]
