A rectangular garden has a length 3 times its width. If the perimeter is 64 meters, what is the area of the garden? - Redraw
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:
📰 Sawur Never Ends: When Job Hunt Feels Like Eternal Embrace 📰 Dream Job Pulling You Through Sahur: Why This Dream Won’t Let Go 📰 Job Isn’t Done—Sahur’s The Real Sprint For Your Future 📰 Dollar Trend 6454795 📰 Gme Stock Message Board Shockmoment Inside The New Trend Fueling Wallstreet Frenzy 1425485 📰 This Pearl Ring Holds Power No Family Can Explainand Its Calling Out For Someone 372489 📰 Unlock Maximum Flexibility Why Hybrid Cloud Computing Is The Future Of It 3654902 📰 Radius Blast Of Nuclear Fury Scary Truths Behind The Devastation 3131124 📰 Great Duets 4304431 📰 Mpwr Stock Hurls Profitswatch Every Trader Panic And Profit As Prices Skyrocket 8432502 📰 Hulu Finally Bans Adsnow Youll Watch Pure Silence Or Watch It In Pain 6060129 📰 Sean Young Movie List 3629840 📰 Acai Pronouncement 8354373 📰 Connections Hint Nov 5 9896620 📰 Pltrs Gap Building Stock Split Heres Why You Need To Watch The Market Climbs Today 1173943 📰 The Tity Emoji That Made Millions Laugh Andu Yt Engagement Skyrocket 5600715 📰 This Secret Marvel Invasion Shocked Expertswhat Is It Youll Theck Now 8816206 📰 How A Single Tattoo Unleashed My Descent Into Berserk Madness 6915926Final 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:
\[
A = L \ imes W = 24 \ imes 8 = 192 \ ext{ square meters}
\]
