Substitute the given values

Oct 13, 2025 by talynt.org 147 views

The Breath of a Rectangular Park: Unraveling the Mystery of Fencing

In the world of mathematics, problems often arise from real-life scenarios, and one such scenario is the fencing of a rectangular park. Given the breath of the park and the length of wire required to fence it once, we are tasked with finding the length of the park. In this article, we will delve into the world of geometry and algebra to unravel the mystery of the rectangular park's dimensions.

To begin with, let's break down the problem and understand what is being asked. We are given that the breath of the rectangular park is 32 meters. This means that the width of the park is 32 meters. We are also given that 472 meters of wire is required to fence the park once. This implies that the perimeter of the park is 472 meters.

Perimeter of a Rectangle

The perimeter of a rectangle is given by the formula:

P = 2(l + b)

where P is the perimeter, l is the length, and b is the breath (or width).

In this case, we are given that the perimeter is 472 meters, and the breath is 32 meters. We can substitute these values into the formula to get:

472 = 2(l + 32)

To solve for the length, we can start by simplifying the equation:

472 = 2(l + 32)

Subtracting 64 from both sides gives us:

408 = 2l

Dividing both sides by 2 gives us:

l = 204

Therefore, the length of the park is 204 meters.

In conclusion, we have successfully unraveled the mystery of the rectangular park's dimensions. By using the formula for the perimeter of a rectangle and substituting the given values, we were able to solve for the length of the park. This problem demonstrates the importance of understanding geometric formulas and how they can be applied to real-life scenarios.

The problem of finding the length of a rectangular park may seem trivial, but it has real-world applications in various fields such as:

Architecture: When designing buildings or structures, architects need to consider the perimeter and dimensions of the building to ensure that it is feasible and cost-effective.
Landscaping: When designing gardens or parks, landscapers need to consider the perimeter and dimensions of the area to ensure that it is aesthetically pleasing and functional.
Engineering: When designing bridges or other infrastructure, engineers need to consider the perimeter and dimensions of the structure to ensure that it is safe and durable.

When solving problems involving the perimeter of a rectangle, remember to:

Use the correct formula: The formula for the perimeter of a rectangle is P = 2(l + b).
Substitute the given values: Make sure to substitute the given values into the formula to get the correct equation.
Simplify the equation: Simplify the equation by combining like terms and isolating the variable.
Check your units: Make sure to check your units to ensure that they are consistent.

What is the formula for the perimeter of a rectangle? The formula for the perimeter of a rectangle is P = 2(l + b).
How do I solve for the length of a rectangle when given the perimeter and breath? To solve for the length, substitute the given values into the formula, simplify the equation, and isolate the variable.
What are some real-world applications of finding the perimeter of a rectangle? Some real-world applications of finding the perimeter of a rectangle include architecture, landscaping, and engineering.
The Breath of a Rectangular Park: Unraveling the Mystery of Fencing

In the previous article, we unraveled the mystery of the rectangular park's dimensions by finding the length of the park given the breath and the length of wire required to fence it once. In this article, we will address some frequently asked questions related to the problem.

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

A: The formula for the perimeter of a rectangle is P = 2(l + b), where P is the perimeter, l is the length, and b is the breath (or width).

Q: How do I solve for the length of a rectangle when given the perimeter and breath?

A: To solve for the length, substitute the given values into the formula, simplify the equation, and isolate the variable. For example, if the perimeter is 472 meters and the breath is 32 meters, you can substitute these values into the formula to get:

472 = 2(l + 32)

Simplifying the equation gives us:

408 = 2l

Dividing both sides by 2 gives us:

l = 204

Therefore, the length of the park is 204 meters.

Q: What are some real-world applications of finding the perimeter of a rectangle?

A: Some real-world applications of finding the perimeter of a rectangle include:

Architecture: When designing buildings or structures, architects need to consider the perimeter and dimensions of the building to ensure that it is feasible and cost-effective.
Landscaping: When designing gardens or parks, landscapers need to consider the perimeter and dimensions of the area to ensure that it is aesthetically pleasing and functional.
Engineering: When designing bridges or other infrastructure, engineers need to consider the perimeter and dimensions of the structure to ensure that it is safe and durable.

Q: What are some tips and tricks for solving problems involving the perimeter of a rectangle?

A: Some tips and tricks for solving problems involving the perimeter of a rectangle include:

Use the correct formula: The formula for the perimeter of a rectangle is P = 2(l + b).
Substitute the given values: Make sure to substitute the given values into the formula to get the correct equation.
Simplify the equation: Simplify the equation by combining like terms and isolating the variable.
Check your units: Make sure to check your units to ensure that they are consistent.

Q: Can I use the perimeter formula to find the area of a rectangle?

A: No, the perimeter formula is not used to find the area of a rectangle. The area of a rectangle is found using the formula A = l × b, where A is the area, l is the length, and b is the breath.

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

A: The perimeter of a rectangle is the distance around the rectangle, while the area of a rectangle is the amount of space inside the rectangle.

Q: Can I use the perimeter formula to find the dimensions of a rectangle if I know the area and the perimeter?

A: Yes, you can use the perimeter formula to find the dimensions of a rectangle if you know the area and the perimeter. However, you will need to use the formula for the area of a rectangle (A = l × b) to find the length and breath.

In conclusion, we have addressed some frequently asked questions related to the problem of finding the length of a rectangular park given the breath and the length of wire required to fence it once. We hope that this article has provided you with a better understanding of the perimeter formula and its applications.