A rectangular garden has a length 3 times its width. If the perimeter is 64 meters, what is the area of the garden? - Midis
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:
📰 Aber Flaschenvolumen nimmt ab, nicht Anzahl. 📰 Richtiger Weg: Wie oft kann man 729 halbieren, bis Volumen bei ≤1 pro Flasche liegt? 📰 Anzahl der Flaschen = Anzahl der Halbierungen, bis Volumen < 1. 📰 Simplifying Gives 📰 Simply Tap Into Magic Magic The Gatherings Secret Final Fantasy Fusion 📰 Sin2Z 60Circ 1 Rightarrow Sin2Z 60Circ Frac12 📰 Sin2Z Sqrt3 Cos2Z 1 📰 Since A 2 Multiply The Entire Equation By 2 2X2 4X 30 0 📰 Since Cos X Sec X 1 Sin X Csc X 1 And Cos2 X Sin2 X 1 We Get 📰 Since Ei 4Pi Cos4Pi I Sin4Pi 1 And Similarly E I 4Pi 1 We Get 📰 Since Phi 3Theta We Substitute 📰 Since 11 Days Pass Exactly Honesty 276 24 11 With Remainder 12 So Shift By 11 Hours And 12 Minutes 📰 Since 72 242 252 It Is A Right Triangle 📰 Since 88 And 4333 Share No Common Factors Lcm 88 Times 4333 380584 📰 Since Gadgets Cannot Be Sold In Fractions Round Up 167 Gadgets 📰 Since Genomes Must Be Whole Numbers Round To Nearest Whole 479 📰 Since Mario Got Stuck In Paper Chaos Luigis Epic Fix Goes Viral 📰 Since The Number Of Cultures Must Be Whole We Round To 259Final 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:
\[
A = L \ imes W = 24 \ imes 8 = 192 \ ext{ square meters}
\]
