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?

February 17, 2026

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 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.

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]

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}]

Final Answer

The area of the rectangle is 108 square meters.

Why This Problem Matters: Practical Applications

This type of question appears frequently in math class, engineering design, interior planning, and architecture. Understanding how expressions and equations link real-world dimensions helps with tasks like calculating floor space, fencing needs, or material estimates.

SEO Optimization: Key Phrases and Structure

To boost visibility on search engines, this article naturally incorporates high-traffic keywords such as:

rectangle area- solving rectangle perimeter- algebra geometry problems- length = 3 times width- perimeter and area calculation- math word problem solution

Headings like “How to Find a Rectangle’s Area from Perimeter and Ratio” and “Step-by-Step: Finding Rectangle Area Given Length and Width Relationship” improve search relevance. Including answer boxes, bullet points, and clear explanations supports readability and boosts SEO performance.

Summary

A rectangle with length 3 times its width and perimeter 48 meters has dimensions 18m × 6m- Its area is 108 square meters- This problem teaches algebraic translation, ratio application, and basic geometry- Optimized for search with relevant keywords and structured content

Whether you’re a student, teacher, or homeowner, mastering this problem strengthens spatial reasoning and mathematical fluency—key skills for everyday and professional success.

Tagline:Solve geometry with confidence—master rectangle puzzles through clear math, real formulas, and practical application.

Keywords: rectangle area, perimeter formula, length three times width, algebra word problem, square meter calculation, math tutoring, geometry practice, home improvement calculations

Meta description: Learn how to calculate the area of a rectangle when length is three times the width and the perimeter is 48 meters. Step-by-step solution with formula breakdown and real-world relevance.