Calculating the Total Border Length

Oct 13, 2025 by windailys.com 29 views

Problem Overview

Isabelle is planning to create a beautiful rectangular flower bed in her garden. However, she wants to add a border around it, but one long side will be next to the house and will not have a border. This means that the border will only be applied to three sides of the flower bed. The longer side of the flower bed is twice the shorter side, and Isabelle has 24 feet of border material. In this article, we will help Isabelle find the length and width of the flower bed.

Understanding the Problem

To solve this problem, we need to understand the relationship between the length and width of the flower bed. Let's assume that the shorter side of the flower bed is represented by the variable 'x'. Since the longer side is twice the shorter side, the longer side can be represented by the variable '2x'. The border will be applied to three sides of the flower bed, which are the two shorter sides and the longer side.

Calculating the Total Border Length

The total length of the border is the sum of the lengths of the three sides that will have a border. Since the border will be applied to the two shorter sides and the longer side, the total border length can be represented by the equation:

2x + 2x + 2x = 24

Combine like terms:

6x = 24

Solving for x

To find the value of x, we need to divide both sides of the equation by 6:

x = 24 / 6

x = 4

Finding the Length and Width of the Flower Bed

Now that we have found the value of x, we can find the length and width of the flower bed. Since the shorter side is represented by the variable 'x', the length of the shorter side is 4 feet. Since the longer side is twice the shorter side, the length of the longer side is 2x = 2(4) = 8 feet.

Conclusion

In this article, we helped Isabelle find the length and width of her rectangular flower bed. By understanding the relationship between the length and width of the flower bed and using algebraic equations, we were able to find the value of x, which represents the length of the shorter side. We then used this value to find the length and width of the flower bed, which are 4 feet and 8 feet, respectively.

Real-World Applications

This problem has real-world applications in various fields, such as:

Gardening: When planning a garden, it's essential to consider the size and shape of the garden bed. By understanding the relationship between the length and width of the garden bed, gardeners can create a beautiful and functional garden.
Architecture: Architects use mathematical equations to design buildings and structures. By understanding the relationship between the length and width of a building, architects can create a functional and aesthetically pleasing design.
Engineering: Engineers use mathematical equations to design and build various structures, such as bridges and buildings. By understanding the relationship between the length and width of a structure, engineers can create a safe and functional design.

Tips and Tricks

When solving problems like this, it's essential to:

Read the problem carefully: Make sure to understand the problem and what is being asked.
Use algebraic equations: Algebraic equations can help you solve problems like this by representing the relationship between the length and width of the flower bed.
Check your work: Make sure to check your work to ensure that you have found the correct solution.

Common Mistakes

When solving problems like this, it's essential to avoid common mistakes, such as:

Not reading the problem carefully: Failing to read the problem carefully can lead to incorrect solutions.
Not using algebraic equations: Failing to use algebraic equations can make it difficult to solve the problem.
Not checking your work: Failing to check your work can lead to incorrect solutions.

Conclusion

In conclusion, this problem is a great example of how algebraic equations can be used to solve real-world problems. By understanding the relationship between the length and width of the flower bed and using algebraic equations, we were able to find the length and width of the flower bed. This problem has real-world applications in various fields, such as gardening, architecture, and engineering. By following tips and tricks and avoiding common mistakes, we can solve problems like this with ease.

Frequently Asked Questions

In this article, we will answer some of the most frequently asked questions about Isabelle's rectangular flower bed border.

Q: What is the relationship between the length and width of the flower bed?

A: The longer side of the flower bed is twice the shorter side. This means that if the shorter side is represented by the variable 'x', the longer side can be represented by the variable '2x'.

Q: How do we calculate the total border length?

A: The total border length is the sum of the lengths of the three sides that will have a border. Since the border will be applied to the two shorter sides and the longer side, the total border length can be represented by the equation:

2x + 2x + 2x = 24

Combine like terms:

6x = 24

Q: How do we solve for x?

A: To find the value of x, we need to divide both sides of the equation by 6:

x = 24 / 6

x = 4

Q: What is the length and width of the flower bed?

A: Since the shorter side is represented by the variable 'x', the length of the shorter side is 4 feet. Since the longer side is twice the shorter side, the length of the longer side is 2x = 2(4) = 8 feet.

Q: What are some real-world applications of this problem?

A: This problem has real-world applications in various fields, such as:

Gardening: When planning a garden, it's essential to consider the size and shape of the garden bed. By understanding the relationship between the length and width of the garden bed, gardeners can create a beautiful and functional garden.
Architecture: Architects use mathematical equations to design buildings and structures. By understanding the relationship between the length and width of a building, architects can create a functional and aesthetically pleasing design.
Engineering: Engineers use mathematical equations to design and build various structures, such as bridges and buildings. By understanding the relationship between the length and width of a structure, engineers can create a safe and functional design.

Q: What are some tips and tricks for solving problems like this?

A: When solving problems like this, it's essential to:

Read the problem carefully: Make sure to understand the problem and what is being asked.
Use algebraic equations: Algebraic equations can help you solve problems like this by representing the relationship between the length and width of the flower bed.
Check your work: Make sure to check your work to ensure that you have found the correct solution.

Q: What are some common mistakes to avoid when solving problems like this?

A: When solving problems like this, it's essential to avoid common mistakes, such as:

Not reading the problem carefully: Failing to read the problem carefully can lead to incorrect solutions.
Not using algebraic equations: Failing to use algebraic equations can make it difficult to solve the problem.
Not checking your work: Failing to check your work can lead to incorrect solutions.

Q: Can you provide more examples of how to use algebraic equations to solve problems like this?

A: Yes, here are a few more examples:

Example 1: A rectangular garden bed has a length of 10 feet and a width of 5 feet. If the border is 2 feet wide, what is the total area of the garden bed?
Example 2: A rectangular building has a length of 20 feet and a width of 10 feet. If the border is 3 feet wide, what is the total area of the building?

Q: Can you provide more information about the importance of algebraic equations in real-world applications?

A: Yes, algebraic equations are used in a wide range of real-world applications, including:

Science: Algebraic equations are used to model and solve problems in physics, chemistry, and biology.
Engineering: Algebraic equations are used to design and build various structures, such as bridges and buildings.
Economics: Algebraic equations are used to model and solve problems in economics, such as supply and demand.

Q: Can you provide more information about the benefits of using algebraic equations to solve problems?

A: Yes, using algebraic equations to solve problems has several benefits, including:

Improved accuracy: Algebraic equations can help you solve problems with greater accuracy.
Increased efficiency: Algebraic equations can help you solve problems more quickly and efficiently.
Better understanding: Algebraic equations can help you develop a deeper understanding of the problem and the underlying concepts.