A rectangle has a length that is 4 times its width. If the perimeter of the rectangle is 90 meters, what is the area of the rectangle?
["How to Find the Area of a Rectangle When Perimeter and Length-to-Width Relationship Are Known", "Understanding the relationship between a rectangle’s length, width, and perimeter is essential for solving geometry problems efficiently. One classic problem involves a rectangle where the length is four times the width, and the perimeter is 90 meters. This article breaks down the steps to find the area, helping students and DIY enthusiasts master fundamental math concepts with real-world applications.", "---", "### Step-by-Step: Finding the Area From Perimeter and Side Relationship", "When dealing with rectangular shapes, knowing how to convert textual relationships into mathematical formulas is key. In this problem:", "- The length (L) is 4 times the width (W) → ( L = 4W )\n- The perimeter (P) is 90 meters → ( P = 90 )\n- We need to find the area (A), calculated as ( A = L \ imes W )", "---", "### Step 1: Use the Perimeter Formula", "The perimeter of a rectangle is given by:\n[ P = 2L + 2W ]", "Substitute the known perimeter and the expression for ( L ):\n[\n90 = 2(4W) + 2W\n]\n[\n90 = 8W + 2W\n]\n[\n90 = 10W\n]", "---", "### Step 2: Solve for Width", "Divide both sides by 10:\n[\nW = \frac{90}{10} = 9 \ ext{ meters}\n]", "---", "### Step 3: Find the Length", "Now use ( L = 4W ):\n[\nL = 4 \ imes 9 = 36 \ ext{ meters}\n]", "---", "### Step 4: Calculate the Area", "Area of a rectangle is:\n[\nA = L \ imes W = 36 \ imes 9 = 324 \ ext{ square meters}\n]", "---", "### Why This Matters: Real-World Applications", "This type of problem appears in layouts, construction, agriculture, and design—any field requiring precise space measurement. Knowing how to derive dimensions from constraints streamlines planning and calculations.", "---", "### Final Answer", "With a length of 36 meters and width of 9 meters, the area of the rectangle is:\n324 square meters", "---", "### Key Takeaways", "- Translate word problems into algebraic expressions.\n- Use the perimeter formula ( P = 2(L + W) ) with known ratios.\n- Solve step-by-step to isolate variables.\n- Apply multiplication to find area once dimensions are known.", "Mastering these techniques empowers anyone to tackle geometry challenges confidently. Whether for homework, home projects, or professional work, these skills are both practical and foundational."]
