A rectangle has a length that is 3 times its width. If the perimeter is 64 meters, what is the area of the rectangle?
["Title: How to Find the Area of a Rectangle When Length is Three Times the Width – Solve with Perimeter = 64 m", "---", "Meta Description:\nLearn how to calculate the area of a rectangle with a length 3 times its width, given a perimeter of 64 meters. Step-by-step solution included.", "---", "### Understanding Rectangular Geometry: The Key Formula", "Rectangles are foundational shapes in geometry, defined by two key dimensions: length and width. One important relationship often taught in math classes is when the length is three times the width. This ratio directly influences how we calculate perimeter and area.", "In this article, we’ll explore how to determine the area of a rectangle when:", "- The length ((L)) is 3 times the width ((W)),\n- The perimeter is 64 meters,\n- And you want to find the corresponding area.", "---", "### Step 1: Express Length and Width Using Algebra", "Let’s define the variables based on the given ratio:", "- (\ ext{Width} = W)\n- (\ ext{Length} = 3W) (since length is three times width)", "---", "### Step 2: Use the Perimeter Formula", "The perimeter (P) of a rectangle is given by:", "[\nP = 2(\ ext{Length} + \ ext{Width})\n]", "Substitute the known values:", "[\n64 = 2(3W + W)\n]", "Simplify inside the parentheses:", "[\n64 = 2(4W)\n]", "[\n64 = 8W\n]", "---", "### Step 3: Solve for Width", "Divide both sides by 8:", "[\nW = \frac{64}{8} = 8 \ ext{ meters}\n]", "Now find the length:", "[\nL = 3W = 3 \ imes 8 = 24 \ ext{ meters}\n]", "---", "### Step 4: Calculate the Area", "The area (A) of a rectangle is:", "[\nA = \ ext{Length} \ imes \ ext{Width}\n]", "Substitute the values:", "[\nA = 24 \ imes 8 = 192 \ ext{ square meters}\n]", "---", "### ✅ Final Answer: The area of the rectangle is 192 m²", "---", "### Why This Matters", "Understanding how to translate word problems into equations empowers you to solve real-life geometry challenges—whether designing rooms, calculating building materials, or studying mathematical principles.", "Key takeaway: When a rectangle’s length is 3 times its width and the perimeter is 64 meters, the area is 192 square meters.", "---", "Keywords: rectangle area calculation, perimeter and area rectangle, how to find area from perimeter, rectangle with length 3 times width, math problem solution, geometry problems, rectangle dimensions problem", "---", "Related Articles:\n- Solve rectangle area problems using perimeter\n- How to use algebra to find rectangle dimensions\n- Perimeter and area formulas explained step-by-step", "---", "Want more math tips? Subscribe for updates and deeper dives into geometry and algebra!"]
