Solve The Perimeter Equation For $W$.The Equation For The Perimeter Of A Rectangle Is $P = 2L + 2W$, Where $L$ And $W$ Represent The Length And Width Of The Rectangle.

Introduction

In mathematics, the perimeter of a rectangle is a fundamental concept that is used to calculate the total distance around the shape. The perimeter equation is given by $P = 2L + 2W$, where $L$ and $W$ represent the length and width of the rectangle. In this article, we will focus on solving the perimeter equation for $W$, which is a crucial step in finding the width of the rectangle.

Understanding the Perimeter Equation

The perimeter equation is a simple yet powerful tool that can be used to calculate the total distance around a rectangle. The equation is given by $P = 2L + 2W$, where $P$ is the perimeter, $L$ is the length, and $W$ is the width. To solve for $W$, we need to isolate the variable $W$ on one side of the equation.

Isolating W

To isolate $W$, we need to get rid of the $2W$ term on the right-hand side of the equation. We can do this by subtracting $2W$ from both sides of the equation. This gives us:

$$P - 2W = 2L$$

Next, we need to get rid of the $2W$ term on the left-hand side of the equation. We can do this by adding $2W$ to both sides of the equation. This gives us:

$$P = 2L + 2W$$

Now, we can see that the $2W$ term is on the right-hand side of the equation. To isolate $W$, we need to get rid of the $2$ term that is multiplied by $W$. We can do this by dividing both sides of the equation by $2$. This gives us:

$$\frac{P}{2} = L + W$$

Solving for W

Now that we have isolated $W$, we can solve for $W$ by subtracting $L$ from both sides of the equation. This gives us:

$$W = \frac{P}{2} - L$$

This is the solution to the perimeter equation for $W$. We can see that the width of the rectangle is equal to half of the perimeter minus the length.

Example

Let's say we have a rectangle with a perimeter of $20$ and a length of $6$. We can use the solution to the perimeter equation to find the width of the rectangle.

$$W = \frac{P}{2} - L$$

$$W = \frac{20}{2} - 6$$

$$W = 10 - 6$$

$$W = 4$$

Therefore, the width of the rectangle is $4$.

Conclusion

In this article, we have solved the perimeter equation for $W$, which is a crucial step in finding the width of a rectangle. We have shown that the width of the rectangle is equal to half of the perimeter minus the length. We have also provided an example of how to use the solution to the perimeter equation to find the width of a rectangle. We hope that this article has been helpful in understanding the concept of the perimeter equation and how to solve it for $W$.

Applications of the Perimeter Equation

The perimeter equation has many applications in real-world problems. For example, it can be used to calculate the total distance around a building or a piece of land. It can also be used to calculate the cost of fencing a rectangular area. In addition, the perimeter equation can be used to solve problems involving the area and perimeter of a rectangle.

Real-World Examples

1. Fencing a Rectangular Area: Suppose we want to fence a rectangular area with a perimeter of $100$ feet. We can use the solution to the perimeter equation to find the width of the rectangle.

$$W = \frac{P}{2} - L$$

$$W = \frac{100}{2} - 20$$

$$W = 50 - 20$$

$$W = 30$$

Therefore, the width of the rectangle is $30$ feet.

2. Calculating the Cost of Fencing: Suppose we want to fence a rectangular area with a perimeter of $100$ feet. The cost of fencing is $5$ dollars per foot. We can use the solution to the perimeter equation to find the width of the rectangle and then calculate the total cost of fencing.

$$W = \frac{P}{2} - L$$

$$W = \frac{100}{2} - 20$$

$$W = 50 - 20$$

$$W = 30$$

The total cost of fencing is:

$$Total Cost = 5 \times 100$$

$$Total Cost = 500$$

Therefore, the total cost of fencing is $500$ dollars.

Conclusion

In conclusion, the perimeter equation is a fundamental concept in mathematics that is used to calculate the total distance around a rectangle. We have solved the perimeter equation for $W$, which is a crucial step in finding the width of a rectangle. We have also provided examples of how to use the solution to the perimeter equation to solve real-world problems. We hope that this article has been helpful in understanding the concept of the perimeter equation and how to solve it for $W$.