Question**: A rectangle's length is three times its width. If the perimeter of the rectangle is 48 meters, what is the area of the rectangle? - Dyverse
Solving for the Area of a Rectangle: A Practical Math Problem
Solving for the Area of a Rectangle: A Practical Math Problem
When faced with a geometry question like "A rectangle’s length is three times its width, and the perimeter is 48 meters. What is the area?", it’s easy to break the problem down step by step—especially with SEO in mind. This article will guide you through solving this common math challenge while optimizing for search engines to help readers understand both the solution and key terms like rectangle area, perimeter formula, and algebraic modeling.
Understanding the Context
Understanding the Problem
Before solving, it’s important to clearly define the relationship between the rectangle’s dimensions. According to the question:
- The length (L) is three times the width (W)
- That is, ( L = 3W )
- The perimeter (P) is given as 48 meters
- We are asked to find the Area (A) of the rectangle
This setup is ideal for teaching algebraic problem-solving, making it highly relevant for students, educators, and DIY home project planners.
Image Gallery
Key Insights
Step 1: Use the Perimeter Formula
The perimeter of a rectangle is calculated using the formula:
[
P = 2(L + W)
]
Plugging in the known perimeter:
[
48 = 2(L + W)
]
Divide both sides by 2:
[
24 = L + W
]
🔗 Related Articles You Might Like:
📰 Refuse to Miss This Lightning Upgrade in vomero Plus 📰 Unlock Power You Never Knew Was in viral vomero Plus performance! 📰 You Won’t Believe What This Vomero 5 Can Do For Your Home 📰 This Bluto Star Wars Reveal Has Fans Raised Eyebrows Sharp As Lightsabers 📰 This Bmw Wallpaper You Wont Want To Hide17 Surprising Features Inside 📰 This Bna Anime Changed Everything Stream It Before It Vanishes 📰 This Bo7 Calculated Caught Experts Off Guard Inside The Move That Rocked It 📰 This Bo7 Assault Rifle Shocked Soldiersyou Wont Believe Its Firepower 📰 This Boa Sand Is Taking Fashion By Stormshop The Ultimate Stylish Must Have 📰 This Board And Batten Calculator Will Transform Your Home Renovation Costs Overnight 📰 This Board And Batten Wall Transformed Our Homeyou Wont Believe How It Elevated Our Decor 📰 This Board Game Will Revolutionize Your Eveningsheres Why Everyones Obsessed 📰 This Boat And Tote Set Is Taking Outdoor Adventures By Storm 📰 This Boat Drawing Will Blow Your Mind See How Its Done In Just Minutes 📰 This Boat Neck Dress Was Hidden In Your Closetyoull Want It Now 📰 This Boat Neck Frock Will Transform Your Summer Outfits Instantly 📰 This Boat Neck Top Is Changing Fashionshop Before It Disappears 📰 This Boat Tote Will Transform Your Summer Adventuresdont Believe Us Until You See ItFinal Thoughts
Step 2: Substitute the Length in Terms of Width
Since ( L = 3W ), substitute into the sum:
[
24 = 3W + W = 4W
]
Solve for ( W ):
[
W = \frac{24}{4} = 6 \ ext{ meters}
]
Step 3: Find the Length
Using ( L = 3W ):
[
L = 3 \ imes 6 = 18 \ ext{ meters}
]
Step 4: Calculate the Area
The area ( A ) of a rectangle is:
[
A = L \ imes W
]
Substitute the values:
[
A = 18 \ imes 6 = 108 \ ext{ square meters}
]
