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:

  1. The rectangle’s length (L) is three times its width (W):
    L = 3W
  2. 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)

A rectangle's length is triple its width. If the perimeter is 48 meters, what are the dimensions of the rectangle?

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

Continue Reading

\[ \frac{V_s}{V_c} = \frac{36\pi}{24\pi} = \frac{36}{24} = \frac{3}{2} \]
\(\boxed{\frac{3}{2}}\)
Question:** A programmer models a circular sensor with a radius of \(5\) cm. A square with side length equal to the diameter of the circle is inscribed in the circle. What is the circumference of the circle in terms of \(\pi\)?

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Final Thoughts

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