A rectangular garden has a length 3 times its width. If the perimeter is 64 meters, what is the area of the garden?

February 17, 2026

How to Calculate the Area of a Rectangular Garden with a Perimeter of 64 Meters

If you’ve ever been curious about how to find the area of a rectangular garden from its perimeter and a ratio between its length and width, this article is for you. Today, we’ll solve a classic geometry problem: a rectangular garden where the length is three times the width, and the total perimeter is 64 meters. What’s the garden’s area? Let’s break it down step-by-step for clear understanding and practical insight.

Understanding the Problem

We know:- The length \( L \) is 3 times the width \( W \), so: \( L = 3W \)- The perimeter \( P \) is 64 meters. For a rectangle, perimeter formula is: \( P = 2L + 2W \)

We’ll use these two facts to find \( L \) and \( W \), then compute the area \( A = L \ imes W \).

Step 1: Substitute and Set Up the Equation

Substitute \( L = 3W \) into the perimeter formula:

\[P = 2L + 2W = 2(3W) + 2W = 6W + 2W = 8W\]

Given \( P = 64 \) meters, set up the equation:

\[8W = 64\]

Step 2: Solve for Width

Divide both sides by 8:

\[W = \frac{64}{8} = 8 \ ext{ meters}\]

Now find the length:

\[L = 3W = 3 \ imes 8 = 24 \ ext{ meters}\]

Step 3: Calculate the Area

Use the area formula for a rectangle:

\[A = L \ imes W = 24 \ imes 8 = 192 \ ext{ square meters}\]

Final Answer

The rectangular garden has a width of 8 meters, a length of 24 meters, and an area of 192 square meters.

Bonus: Why This Matters

Understanding how to calculate area from perimeter and proportions is essential in gardening, landscaping, architecture, and urban planning. Whether you're designing a small backyard plot or a community green space, knowing these formulas helps optimize space and materials efficiently.

In summary, a rectangular garden with a length 3 times its width and a 64-meter perimeter measures 24 meters by 8 meters, yielding a total area of 192 m². Use this simple yet powerful geometry insight to bring your garden dreams to life!