A rectangular garden has a length 3 times its width. If the perimeter is 64 meters, what is the area of the garden? - Coaching Toolbox
How to Calculate the Area of a Rectangular Garden with a Perimeter of 64 Meters
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 Context
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 \( A = L \ imes W \).
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Key Insights
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:
\[
8W = 64
\]
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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:
\[
A = L \ imes W = 24 \ imes 8 = 192 \ ext{ square meters}
\]
