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? - Redraw
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:
📰 weather in yosemite national park 📰 turning red 2 📰 all clad factory seconds 📰 Self Directed Retirement Account 6779255 📰 Auto Aim For Roblox 9798897 📰 Royal Meadows 1157876 📰 This Movie Movie New Agency Is Ruining Theaterssee What Everyones Discussing 3052076 📰 Caught On Camera The Director General Of Audit Exposed The Unthinkable 1082842 📰 Seedot Revealed The Hidden Hack That Took The Internet By Storm 729262 📰 Oregon Ducks Game On What Channel 6911466 📰 The Shocking Truth About Why Its Now Officially A Bigger City 4312113 📰 This Is How Gol D Roger Finally Rewrote Legendary Historyshocking Proof Revealed 9459626 📰 Fourth Largest Scottish City 8172262 📰 Allis Surprise Slam Did Nigeria Lose The Player Who Changed Everything 8488225 📰 Master Every Piano Song Fastdownload The Ultimate Chord Chart Now 76356 📰 Prepare Phone For Trade In Verizon 1423974 📰 Doubletree By Hilton Cherry Hill Philadelphia 9843737 📰 Sq Ft To Sq Metre 1793311Final 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}
]
