A rectangle has a length that is 3 times its width. If the perimeter is 48 meters, find the area of the rectangle.
["How to Find the Area of a Rectangle When Length Is Three Times Its Width – A Practical Example (Perimeter 48m)", "When solving geometry problems involving rectangles, understanding the relationship between length, width, perimeter, and area is essential. One classic scenario is when the length is three times the width, and the perimeter is known — a problem often encountered in math classes and real-life applications. In this article, we’ll walk through a step-by-step solution to find the area of the rectangle given these conditions.", "---", "### Problem Statement", "A rectangle has a length that is 3 times its width, and its perimeter is 48 meters.\nQuestion: What is the area of the rectangle?", "---", "### Understanding the Formula", "First, recall the key formulas related to rectangles:", "- Perimeter = 2(length + width)\n- Area = length × width", "Let the width of the rectangle be ( w ) meters.\nSince the length is 3 times the width, the length ( l = 3w ).", "Using the perimeter formula:", "[\n\ ext{Perimeter} = 2(l + w) = 2(3w + w) = 2(4w) = 8w\n]", "We know the perimeter is 48 meters:", "[\n8w = 48\n]", "---", "### Solving for Width", "Divide both sides by 8:", "[\nw = \frac{48}{8} = 6 \ ext{ meters}\n]", "Now, calculate the length:", "[\nl = 3w = 3 \ imes 6 = 18 \ ext{ meters}\n]", "---", "### Calculating the Area", "Now, use the area formula:", "[\n\ ext{Area} = \ ext{length} \ imes \ ext{width} = 18 \ imes 6 = 108 \ ext{ square meters}\n]", "---", "### Final Answer", "The area of the rectangle is 108 square meters.", "---", "### Summary", "| Step | Calculation |\n|----------------------|----------------------------------|\n| Let width = ( w ) | ( w ) |\n| Length = ( 3w ) | ( l = 3w ) |\n| Perimeter formula | ( 2(l + w) = 48 ) |\n| Solve for ( w ) | ( 8w = 48 \Rightarrow w = 6 ) |\n| Calculate length | ( l = 3 \ imes 6 = 18 ) |\n| Find area | ( 18 \ imes 6 = 108 , \ ext{m}^2 ) |", "---", "### Why This Matters", "Knowing how to connect dimensions with perimeter and area helps in solving real-world problems — from designing rooms to planning garden layouts. Understanding that when length = 3 × width and perimeter = 48 m, the area comes out neatly to 108 m², makes math accessible and practical.", "---", "### Key Takeaways", "- Use algebra to express relationships: ( l = 3w )\n- Apply perimeter formula to solve for width\n- Use area formula with known values\n- Simple substitution makes complex problems manageable", "---", "### Get Practicing!", "Try similar problems:\n- If perimeter is 60 m, length = 4x width → What’s the area?\nUse the method shown above to practice step-by-step solution-building.", "---", "Learn geometry by solving equations. A rectangle’s dimensions reveal its area when relationships are clear. ✅", "---", "Keywords: rectangle area, length 3 times width, perimeter 48 meters, geometry problem, algebra geometry, rectangle dimensions, how to find rectangle area, math homework help"]
