A rectangle has a length that is 4 times its width. If the perimeter of the rectangle is 90 meters, find the area of the rectangle.
["# Finding the Area of a Rectangle: Length is 4 Times the Width & Perimeter of 90 Meters", "When solving geometry problems involving rectangles, one of the most effective strategies is translating given relationships into mathematical equations. In this article, we’ll explore how to determine the area of a rectangle where the length is 4 times the width and the perimeter is 90 meters. This real-world scenario is common in construction, garden planning, and architectural design, making it a practical and useful example for learners and professionals alike.", "## Understanding the Rectangle Problem", "We are given:\n- The length (( L )) is 4 times the width (( W ))\n- The perimeter (( P )) is 90 meters\n- We need to find the area (( A )) of the rectangle", "### Step 1: Set Up the Relationships Mathematically", "From the problem statement, we can express the length in terms of the width:\n[\nL = 4W\n]", "The formula for the perimeter of a rectangle is:\n[\nP = 2(L + W)\n]", "Substituting the given perimeter:\n[\n90 = 2(L + W)\n]", "Now substitute ( L = 4W ) into the perimeter equation:\n[\n90 = 2(4W + W)\n]\n[\n90 = 2(5W)\n]\n[\n90 = 10W\n]", "### Step 2: Solve for the Width", "[\nW = \frac{90}{10} = 9 \ ext{ meters}\n]", "### Step 3: Find the Length", "Using ( L = 4W ):\n[\nL = 4 \ imes 9 = 36 \ ext{ meters}\n]", "### Step 4: Calculate the Area", "The area of a rectangle is given by:\n[\nA = L \ imes W\n]\n[\nA = 36 \ imes 9 = 324 \ ext{ square meters}\n]", "---", "## Summary", "- Width: 9 meters\n- Length: 36 meters\n- Perimeter: 90 meters (matches given value)\n- Area: 324 square meters", "By defining the relationships between length and width, applying the perimeter formula, and solving step-by-step, we accurately determined that a rectangle with a length 4 times its width and a perimeter of 90 meters has an area of 324 square meters.", "This method proves invaluable for quickly solving similar problems in both academic settings and real-life applications such as interior design, landscaping, and carpentry.", "---", "Key takeaway: Always translate word problems into equations—especially in rectangle problems—and verify your results using the perimeter and area formulas.", "---", "Keywords for SEO: rectangle area calculation, solve rectangle perimeter problem, length is 4 times width, find rectangle area from perimeter, geometry problems with variables, real-world rectangle dimensions."]
