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? - Decision Point
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:
📰 Is Spore About to Crash or Crash? Sharper Moves Behind Its Explosive Share Price! 📰 Sport Cloud: The Secret Weapon Every Pro Athlete Uses to Stay Ahead! 📰 From Gamers to Athletes: Sport Cloud Proves Why Cloud Power Dominates Sport! 📰 Why All Chef Influencers Are Raving About Pepper Potsyou Must Try Them 3063904 📰 Photo Recognition 3222603 📰 Finally Got Itdraw Mickey Mouse In Less Than 10 Easy Steps 5136996 📰 Gift Of Life Michigan 9485843 📰 Dont Miss These Metro Mattress Stores Closing Soonmaximize Your Deal Today 1602703 📰 Wrestler Dies 6826891 📰 Watch Turtles All The Way Down 1908740 📰 Nutty Putty Cave Incident 6922786 📰 Marvels Guardians Of The Galaxy The Untold Secrets That Prove This Reel Is Iconic 2448607 📰 Credit Convey 5818302 📰 This Secret R34 Leak In Fortnite Is Otherwise Forbidden 1052647 📰 Act Fast 529 Max 250K Contribution Rule You Wont Believe Changes Goals Forever 6964694 📰 Foodways Definition 2749059 📰 Paradise Liquor 777996 📰 Double The Flavor Half The Cleanup One Pan Chicken Recipes You Need To Try Now 9032078Final 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}
]
