A rectangle's length is triple its width. If the perimeter is 48 meters, what are the dimensions of the rectangle?
Title: Solve for a Rectangle with Triple Length-to-Width Ratio & 48-Meter Perimeter – Find Dimensions Now!
When dealing with geometric problems, especially involving rectangles, understanding how relationships between length, width, and perimeter unlocks quick solutions. In this article, we’ll explore a classic problem: a rectangle where the length is three times its width and the perimeter is 48 meters. Whether you’re a student, teacher, or DIY enthusiast, this breakdown will help you calculate the dimensions easily and understand the math behind it.
Understanding the Problem
We know two key facts:
- The rectangle’s length (L) is three times its width (W): L = 3W
- The perimeter (P) of the rectangle is 48 meters.
For any rectangle, the perimeter is calculated with the formula: P = 2 × (Length + Width) Substituting the known formula, we get: 48 = 2 × (L + W)
Step-by-Step Solution
Step 1: Substitute Length in Perimeter Formula
Since L = 3W, replace L in the perimeter equation: 48 = 2 × (3W + W)
Step 2: Simplify the Equation
Add the terms inside the parentheses: 48 = 2 × (4W) → 48 = 8W
Step 3: Solve for Width
Divide both sides by 8: W = 48 ÷ 8 = 6 meters
Step 4: Calculate Length
Now use L = 3W: L = 3 × 6 = 18 meters
Final Dimensions
- Width = 6 meters
- Length = 18 meters
Why This Matters
Knowing how to derive dimensions from perimeter, ratio, or area helps in architectural design, landscaping, manufacturing, and everyday planning. For example, if designing a rectangular garden with a fixed fence length of 48 meters and a width-to-length ratio of 1:3, you now know the exact space you’re working with — exactly 6 meters wide and 18 meters long.
Quick Recap
| Parameter | Value | |----------|-----------| | Width (W) | 6 meters | | Length (L) | 18 meters | | Perimeter (P) | 48 meters | | Ratio (L:W) | 3:1 |
Bottom Line
When you know the relationship between length and width, plus the perimeter, calculating a rectangle’s dimensions is straightforward. Using simple algebra—substituting and solving—yields clean results every time. Next time you’re faced with a rectangle problem, apply this method: define variables based on given ratios, plug into the perimeter formula, and solve. Your rectangle dimensions will follow quickly!
Keywords: rectangle dimensions, perimeter formula, length and width relationship, solve rectangle problems, geometry problem solving, 48-meter perimeter rectangle, width to length ratio, rectangular garden dimensions, math practice for students.
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