A rectangle's length is triple its width. If the perimeter is 48 meters, what are the dimensions of the rectangle? - Decision Point
Title: Solve for a Rectangle with Triple Length-to-Width Ratio & 48-Meter Perimeter – Find Dimensions Now!
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 Context
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)
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Key Insights
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
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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 |
