Understanding Perimeter and Dimensions

Oct 13, 2025 by thesweetdesigns.com 123 views

Introduction

In the realm of mathematics, rectangles are fundamental shapes that play a crucial role in various mathematical concepts, including geometry and algebra. One of the essential properties of a rectangle is its perimeter, which is the total distance around its edges. In this article, we will delve into the world of rectangles and explore how to find the width of a rectangle given its perimeter and length.

Understanding Perimeter and Dimensions

Before we dive into the problem, let's first understand the concepts of perimeter and dimensions. The perimeter of a rectangle is calculated by adding the lengths of all its sides. Since a rectangle has two pairs of equal sides, its perimeter can be calculated using the formula:

Perimeter = 2(length + width)

The dimensions of a rectangle refer to its length and width. In this case, we are given the length of the rectangle, which is 35 cm.

The Problem

A rectangle has a perimeter of 84 cm and a length of 35 cm. What is its width?

Step 1: Write Down the Formula for Perimeter

The formula for the perimeter of a rectangle is:

Perimeter = 2(length + width)

Step 2: Plug in the Given Values

We are given the perimeter (84 cm) and the length (35 cm). We can plug these values into the formula:

84 = 2(35 + width)

Step 3: Simplify the Equation

To simplify the equation, we can start by dividing both sides by 2:

42 = 35 + width

Step 4: Solve for Width

Now, we can solve for the width by subtracting 35 from both sides:

width = 42 - 35 width = 7

Conclusion

In this article, we have explored how to find the width of a rectangle given its perimeter and length. By using the formula for perimeter and plugging in the given values, we were able to solve for the width. The width of the rectangle is 7 cm.

Real-World Applications

Understanding how to find the width of a rectangle has numerous real-world applications. For example, in architecture, knowing the dimensions of a building or a room is crucial for designing and constructing it. In engineering, understanding the dimensions of a machine or a structure is essential for its design and functionality.

Tips and Tricks

Here are some tips and tricks to help you solve problems like this:

Always read the problem carefully and understand what is given and what is asked.
Use the formula for perimeter and plug in the given values.
Simplify the equation by dividing both sides by a common factor.
Solve for the unknown variable by isolating it on one side of the equation.

Common Mistakes

Here are some common mistakes to avoid when solving problems like this:

Not reading the problem carefully and misunderstanding what is given and what is asked.
Not using the formula for perimeter and plugging in the given values.
Not simplifying the equation by dividing both sides by a common factor.
Not solving for the unknown variable by isolating it on one side of the equation.

Conclusion

In conclusion, finding the width of a rectangle given its perimeter and length is a fundamental concept in mathematics. By using the formula for perimeter and plugging in the given values, we can solve for the width. Understanding how to find the width of a rectangle has numerous real-world applications and is an essential skill to have in mathematics.

Final Thoughts

In this article, we have explored how to find the width of a rectangle given its perimeter and length. We have also discussed the importance of understanding the dimensions of a rectangle and how it applies to real-world scenarios. By following the steps outlined in this article, you should be able to solve problems like this with ease.

Additional Resources

If you are looking for additional resources to help you understand how to find the width of a rectangle, here are some suggestions:

Khan Academy: Perimeter and Area of Rectangles
Mathway: Perimeter of a Rectangle
IXL: Perimeter of a Rectangle

Frequently Asked Questions

Here are some frequently asked questions related to finding the width of a rectangle:

Q: What is the formula for the perimeter of a rectangle? A: The formula for the perimeter of a rectangle is: Perimeter = 2(length + width)
Q: How do I find the width of a rectangle given its perimeter and length? A: To find the width of a rectangle given its perimeter and length, use the formula for perimeter and plug in the given values. Simplify the equation by dividing both sides by a common factor and solve for the unknown variable.
Q: What are some real-world applications of finding the width of a rectangle? A: Understanding how to find the width of a rectangle has numerous real-world applications, including architecture, engineering, and design.

Introduction

In our previous article, we explored how to find the width of a rectangle given its perimeter and length. In this article, we will delve into a Q&A session, where we will answer some of the most frequently asked questions related to finding the width of a rectangle.

Q&A Session

Q1: What is the formula for the perimeter of a rectangle?

A1: The formula for the perimeter of a rectangle is: Perimeter = 2(length + width)

Q2: How do I find the width of a rectangle given its perimeter and length?

A2: To find the width of a rectangle given its perimeter and length, use the formula for perimeter and plug in the given values. Simplify the equation by dividing both sides by a common factor and solve for the unknown variable.

Q3: What are some real-world applications of finding the width of a rectangle?

A3: Understanding how to find the width of a rectangle has numerous real-world applications, including architecture, engineering, and design. For example, in architecture, knowing the dimensions of a building or a room is crucial for designing and constructing it.

Q4: Can I use the formula for perimeter to find the width of a rectangle if I only know the perimeter and the width?

A4: No, you cannot use the formula for perimeter to find the width of a rectangle if you only know the perimeter and the width. The formula for perimeter requires both the length and the width to be known.

Q5: How do I find the length of a rectangle given its perimeter and width?

A5: To find the length of a rectangle given its perimeter and width, use the formula for perimeter and plug in the given values. Simplify the equation by dividing both sides by a common factor and solve for the unknown variable.

Q6: Can I use the formula for area to find the width of a rectangle?

A6: No, you cannot use the formula for area to find the width of a rectangle. The formula for area requires both the length and the width to be known.

Q7: What is the difference between the perimeter and the area of a rectangle?

A7: The perimeter of a rectangle is the total distance around its edges, while the area of a rectangle is the amount of space inside the rectangle.

Q8: Can I use the formula for perimeter to find the width of a rectangle if I only know the perimeter and the area?

A8: No, you cannot use the formula for perimeter to find the width of a rectangle if you only know the perimeter and the area. The formula for perimeter requires both the length and the width to be known.

Q9: How do I find the area of a rectangle given its perimeter and width?

A9: To find the area of a rectangle given its perimeter and width, use the formula for area and plug in the given values. Simplify the equation by dividing both sides by a common factor and solve for the unknown variable.

Q10: Can I use the formula for perimeter to find the width of a rectangle if I only know the perimeter and the length?

A10: Yes, you can use the formula for perimeter to find the width of a rectangle if you only know the perimeter and the length.

Conclusion

In this Q&A article, we have answered some of the most frequently asked questions related to finding the width of a rectangle. We have also discussed the importance of understanding the dimensions of a rectangle and how it applies to real-world scenarios. By following the steps outlined in this article, you should be able to solve problems like this with ease.

Final Thoughts

Additional Resources

If you are looking for additional resources to help you understand how to find the width of a rectangle, here are some suggestions:

Khan Academy: Perimeter and Area of Rectangles
Mathway: Perimeter of a Rectangle
IXL: Perimeter of a Rectangle

Frequently Asked Questions

Here are some frequently asked questions related to finding the width of a rectangle:

Q: What is the formula for the perimeter of a rectangle? A: The formula for the perimeter of a rectangle is: Perimeter = 2(length + width)
Q: How do I find the width of a rectangle given its perimeter and length? A: To find the width of a rectangle given its perimeter and length, use the formula for perimeter and plug in the given values. Simplify the equation by dividing both sides by a common factor and solve for the unknown variable.
Q: What are some real-world applications of finding the width of a rectangle? A: Understanding how to find the width of a rectangle has numerous real-world applications, including architecture, engineering, and design.

Tips and Tricks

Here are some tips and tricks to help you solve problems like this:

Always read the problem carefully and understand what is given and what is asked.
Use the formula for perimeter and plug in the given values.
Simplify the equation by dividing both sides by a common factor.
Solve for the unknown variable by isolating it on one side of the equation.

Common Mistakes

Here are some common mistakes to avoid when solving problems like this:

Not reading the problem carefully and misunderstanding what is given and what is asked.
Not using the formula for perimeter and plugging in the given values.
Not simplifying the equation by dividing both sides by a common factor.
Not solving for the unknown variable by isolating it on one side of the equation.