The perimeter is given by \( 2(w + 4w) = 90 \).

["Optimize Your Geometry Skills: Solving Perimeter Problems Like a Pro", "Understanding how to calculate the perimeter of a shape is a fundamental skill in geometry and plays a crucial role in real-world applications—from construction and landscaping to graphic design and architecture. One common problem students encounter involves perimeter formulas with variables. Let’s explore a classic example: The perimeter is given by ( 2(w + 4w) = 90 ). This type of equation helps build problem-solving skills that are valuable in both academics and everyday life.", "---", "### What Is Perimeter and Why Does It Matter?", "Perimeter refers to the total length around the outside of a two-dimensional shape. In simple terms, it represents the total distance you would walk if you walked all the way around the figure. For rectangles, the perimeter formula is:", "[\nP = 2(l + w)\n]", "where ( l ) is the length and ( w ) is the width. This formula becomes especially useful when one dimension is a multiple of the other, as seen in our example.", "---", "### Step-by-Step Solution: Solving ( 2(w + 4w) = 90 )", "Let’s break down how to solve the equation ( 2(w + 4w) = 90 ) step-by-step.", "Step 1: Simplify the expression inside the parentheses", "[\nw + 4w = 5w\n]", "So the equation becomes:", "[\n2(5w) = 90\n]", "Step 2: Multiply inside the parentheses", "[\n10w = 90\n]", "Step 3: Solve for ( w )", "[\nw = \frac{90}{10} = 9\n]", "Step 4: Calculate the length", "Given ( w = 9 ), and since length is ( 4w ):", "[\nl = 4w = 4 \ imes 9 = 36\n]", "Step 5: Verify the perimeter", "Using ( P = 2(w + l) ):", "[\nP = 2(9 + 36) = 2 \ imes 45 = 90\n]", "The solution checks out!", "---", "### Why This Problem Is More Than Just Math", "This type of perimeter problem develops essential skills:", "- Algebraic thinking: Translating word problems into equations and solving them.\n- Pattern recognition: Identifying repeated factors (like ( w + 4w = 5w )) simplifies complex expressions.\n- Real-world relevance: Perfect for projects requiring area measurement, material estimation, or spatial reasoning.", "---", "### Practice Makes Perfect", "Want to master perimeter calculations? Try these variations:", "- If ( 2(w + 3w) = 72 ), what is ( w )?\n- A rectangle has width ( 5 ) units. If perimeter is ( 2(w + 4w) ), what is the length?", "Use these exercises to strengthen your understanding and boost confidence in geometry.", "---", "### Final Thoughts", "Mastering perimeter problems using algebraic methods like ( 2(w + 4w) = 90 ) is more than an academic exercise—it’s a foundation for spatial logic and practical problem-solving. Whether you’re designing a garden, calculating fencing needs, or tackling math tests, knowing how to translate shapes into equations empowers you to learn smarter and work more efficiently.", "Keep practicing, stay curious, and watch your geometry skills grow!", "---", "Keywords: perimeter, geometry, algebra, solving equations, word problem, rectangle perimeter, math practice, curriculum problem, real-world application.\nMeta description: Learn how to solve perimeter problems like ( 2(w + 4w) = 90 ), step-by-step. Understand the math behind calculating shapes and build confidence in algebra and geometry."]