Finding Equivalent Expressions

Oct 13, 2025 by recoveryshake.com 14 views

Introduction

When it comes to calculating the perimeter of a square playground surrounded by a sidewalk, we need to consider the length of the sidewalk on each side of the playground. In this article, we will explore how to find two equivalent expressions for the perimeter of the playground, taking into account the width of the sidewalk.

Understanding the Problem

The problem states that the sidewalk surrounding the playground is $2n + 3$ yards long on each side, and the sidewalk itself is $0.5$ yards wide. To find the perimeter of the playground, we need to consider the length of the sidewalk on each side, as well as the width of the sidewalk.

Calculating the Perimeter

The perimeter of a square is calculated by adding up the lengths of all four sides. In this case, we have a square playground surrounded by a sidewalk, so we need to add up the lengths of the sidewalk on each side, as well as the width of the sidewalk.

Let's start by calculating the length of the sidewalk on each side of the playground. Since the sidewalk is $2n + 3$ yards long on each side, we can represent this as:

Sidewalk Length: $2n + 3$

Next, we need to add the width of the sidewalk to the length of the sidewalk on each side. Since the sidewalk is $0.5$ yards wide, we can represent this as:

Sidewalk Width: $0.5$

Now, let's calculate the total length of the sidewalk on each side of the playground by adding the sidewalk length and the sidewalk width:

Total Sidewalk Length: $(2n + 3) + 0.5$

To simplify this expression, we can combine the constants:

Total Sidewalk Length: $2n + 3.5$

Finding Equivalent Expressions

Now that we have calculated the total length of the sidewalk on each side of the playground, we can find two equivalent expressions for the perimeter of the playground.

The perimeter of a square is calculated by adding up the lengths of all four sides. Since we have a square playground surrounded by a sidewalk, we need to add up the lengths of the sidewalk on each side, as well as the width of the sidewalk.

Let's start by calculating the perimeter of the playground using the total sidewalk length:

Perimeter: $4 \times (2n + 3.5)$

To simplify this expression, we can multiply the constants:

Perimeter: $8n + 14$

Now, let's find another equivalent expression for the perimeter of the playground. We can start by calculating the length of the sidewalk on each side of the playground, and then add the width of the sidewalk:

Perimeter: $4 \times (2n + 3) + 4 \times 0.5$

To simplify this expression, we can multiply the constants:

Perimeter: $8n + 12 + 2$

Combining the constants, we get:

Perimeter: $8n + 14$

Conclusion

In this article, we have explored how to find two equivalent expressions for the perimeter of a square playground surrounded by a sidewalk. We started by calculating the length of the sidewalk on each side of the playground, and then added the width of the sidewalk to find the total length of the sidewalk on each side. We then used this total length to find two equivalent expressions for the perimeter of the playground.

By following these steps, we can find equivalent expressions for the perimeter of the playground, taking into account the width of the sidewalk.

Key Takeaways

The perimeter of a square is calculated by adding up the lengths of all four sides.
To find the perimeter of a square playground surrounded by a sidewalk, we need to add up the lengths of the sidewalk on each side, as well as the width of the sidewalk.
We can find two equivalent expressions for the perimeter of the playground by calculating the total length of the sidewalk on each side, and then multiplying by 4 to get the perimeter.

Final Answer

The two equivalent expressions for the perimeter of the playground are:

$8n + 14$
$8n + 12 + 2$

These expressions are equivalent because they both represent the perimeter of the playground, taking into account the width of the sidewalk.

Introduction

In our previous article, we explored how to find two equivalent expressions for the perimeter of a square playground surrounded by a sidewalk. We calculated the length of the sidewalk on each side of the playground, added the width of the sidewalk, and then multiplied by 4 to get the perimeter.

In this article, we will answer some frequently asked questions about the perimeter of a square playground surrounded by a sidewalk.

Q&A

Q: What is the perimeter of a square playground surrounded by a sidewalk?

A: The perimeter of a square playground surrounded by a sidewalk is calculated by adding up the lengths of all four sides. We can find two equivalent expressions for the perimeter by calculating the total length of the sidewalk on each side, and then multiplying by 4.

Q: How do I calculate the total length of the sidewalk on each side of the playground?

A: To calculate the total length of the sidewalk on each side of the playground, we need to add the length of the sidewalk to the width of the sidewalk. The length of the sidewalk is $2n + 3$ yards, and the width of the sidewalk is $0.5$ yards.

Q: What is the formula for the perimeter of a square playground surrounded by a sidewalk?

A: The formula for the perimeter of a square playground surrounded by a sidewalk is:

Perimeter: $4 \times (2n + 3.5)$

Perimeter: $8n + 14$

Q: How do I simplify the expression for the perimeter?

A: To simplify the expression for the perimeter, we can multiply the constants. For example, if we have the expression:

Perimeter: $4 \times (2n + 3) + 4 \times 0.5$

We can simplify it by multiplying the constants:

Perimeter: $8n + 12 + 2$

Combining the constants, we get:

Perimeter: $8n + 14$

Q: What is the difference between the two equivalent expressions for the perimeter?

A: The two equivalent expressions for the perimeter are:

$8n + 14$
$8n + 12 + 2$

The only difference between these two expressions is the way they are written. Both expressions represent the same value, which is the perimeter of the playground.

Q: How do I use the equivalent expressions for the perimeter in real-world applications?

A: The equivalent expressions for the perimeter can be used in a variety of real-world applications, such as:

Calculating the cost of materials needed to build a fence around a playground
Determining the amount of time it will take to walk around a playground
Calculating the area of a playground

Conclusion

In this article, we have answered some frequently asked questions about the perimeter of a square playground surrounded by a sidewalk. We have provided formulas and examples to help illustrate the concepts, and have discussed the importance of equivalent expressions in real-world applications.

Key Takeaways

The perimeter of a square playground surrounded by a sidewalk is calculated by adding up the lengths of all four sides.
We can find two equivalent expressions for the perimeter by calculating the total length of the sidewalk on each side, and then multiplying by 4.
The two equivalent expressions for the perimeter are $8n + 14$ and $8n + 12 + 2$ .
The equivalent expressions for the perimeter can be used in a variety of real-world applications.

Final Answer

The perimeter of a square playground surrounded by a sidewalk is calculated by adding up the lengths of all four sides. We can find two equivalent expressions for the perimeter by calculating the total length of the sidewalk on each side, and then multiplying by 4. The two equivalent expressions for the perimeter are $8n + 14$ and $8n + 12 + 2$ .