Perimeter = 2(x + 3x) = 8x = 64 → x = 8.

How to Solve Perimeter Problems Like Perimeter = 2(x + 3x) = 8x = 64 → x = 8: A Step-by-Step Guide

Understanding perimeter problems is essential for mastering geometry, especially in algebra. Whether you’re solving math homework or tackling real-world measurement challenges, knowing how to simplify expressions and isolate variables is key. In this article, we’ll explore how solving the equation Perimeter = 2(x + 3x) = 8x = 64 → x = 8 works step-by-step, helping you confidently handle similar perimeter problems.

Understanding the Context

Understanding the Perimeter Equation

In geometry, the perimeter of a shape is the total distance around its edges. For polygons such as rectangles, perimeter can be calculated using formulas based on side lengths.

In our example:
Given the perimeter expression:
Perimeter = 2(x + 3x) = 8x
and Perimeter = 64, we set up the equation:
8x = 64

This equation tells us that eight times a variable x equals 64. Our goal is to find the value of x, which represents a fundamental length in this shape.

Perimeter = 2(x + 3x) = 8x = 64 → x = 8.

Key Insights

Step 1: Simplify the Expression Inside Parentheses

Start with:
2(x + 3x)

First, simplify inside the parentheses:
x + 3x = 4x

Now the equation becomes:
2(4x) = 64

🔗 Related Articles You Might Like:

📰 Blackheart Exposed: The Terrifying Truth Behind the Legend You Never Saw Coming 📰 From Myth to Reality: The Shocking Story of Blackheart That Will Blow Your Mind! 📰 Shock the Internet: Meet the Legendary BlackNose Sheep That Oddes Every Farmer! 📰 This Bubly Sparkling Water Looks Magicalheres Why Everyones Obsessed 📰 This Buc Ees Food Menu Has Ice Cream Cravings Sorteddenthalt You With These Famous Dishes 📰 This Bucatini Cacio E Pepe Recipe Clearly Rules Every Dining Tableheres The Magic 📰 This Bucket List Bootcamp Will Turn Your Dreams Into Reality Overnight 📰 This Buddha Board Strategy Will Transform Your Meditation Practice Overnight 📰 This Buddy Daddies Anime Viral On Tiktokwhat Makes It So Addictive 📰 This Budget Bud Vase Is Taking Home Decor By Storm Heres How 📰 This Budget Fashion Brand Just Won Over The Worldbudew Is Evolving Forever 📰 This Buff Orpington Shrinks Your Backyards Sizesee Why Owners Love Him 📰 This Buff Rub Could Double Your Glow In One Applicationyou Wont Believe How Fast It Works 📰 This Buffalo Bill Message Board Message Has Users Going Crazy Foreverdont Miss It 📰 This Buffalo Billions Stanley Insider Reveals The Shocking Secrets Behind His Record Breaking Financial Rise 📰 This Buffalo Chicken Dip With Franks Sauce Is The Ultimate Game Changer At Party Time 📰 This Buffalo Chicken Salad Is So Good Youll Crave It Every Day Cluated Here 📰 This Buffalo Chicken Sandwich Got Everyone Raving Heres Why Youre Addicted

Final Thoughts

Which simplifies to:
8x = 64

Step 2: Solve for x

To isolate x, divide both sides of the equation by 8:
8x ÷ 8 = 64 ÷ 8
x = 8

This shows that the value of x is 8 — a crucial piece of information for finding actual side lengths.

Step 3: Verify the Solution

Plug x = 8 back into the original expression to confirm:
Perimeter = 2(x + 3x) = 2(8 + 3×8) = 2(8 + 24) = 2×32 = 64

The math checks out — the perimeter is indeed 64 when x = 8.