A rectangular garden has a length 3 times its width. If the perimeter is 64 meters, what is the area of the garden? - mm-dev.agency
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 \( A = L \ imes W \).
Image Gallery
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:
\[
8W = 64
\]
🔗 Related Articles You Might Like:
You Miss This Secret Behind Flawless Video Quality in Every Automatic System This Quality Automatic Gadget Is So Smarter It’s Bypassing Every Standard Setup The Only Automatic Quality Solution Proven to Revolutionize Every Screen ExperienceFinal Thoughts
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:
\[
A = L \ imes W = 24 \ imes 8 = 192 \ ext{ square meters}
\]