Which System Of Equations Below Can Be Used To Solve The Following Problem?The Area Of A Rectangular Room Is 156 Square Feet. If The Length Of One Side Of The Room Is 13 Feet, What Is The Perimeter Of The Room?A. 156 = 13 × W 156 = 13 \times W 156 = 13 × W And $P

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Introduction

In mathematics, systems of equations are used to solve problems that involve multiple variables and relationships between them. In this article, we will explore which system of equations can be used to solve the problem of finding the perimeter of a rectangular room given its area and the length of one side.

Understanding the Problem

The problem states that the area of a rectangular room is 156 square feet, and the length of one side of the room is 13 feet. We need to find the perimeter of the room. To do this, we need to use the formula for the area of a rectangle, which is:

Area = Length × Width

We are given the area (156 square feet) and the length (13 feet), so we can use this information to find the width of the room.

System of Equations

There are two possible systems of equations that can be used to solve this problem:

System A

  • 156=13×w156 = 13 \times w
  • P=2×(L+W)P = 2 \times (L + W)

This system of equations is based on the formula for the area of a rectangle and the formula for the perimeter of a rectangle.

System B

  • 156=L×W156 = L \times W
  • P=2×(L+W)P = 2 \times (L + W)

This system of equations is also based on the formula for the area of a rectangle and the formula for the perimeter of a rectangle.

Which System of Equations to Use?

To determine which system of equations to use, we need to examine the given information and the formulas involved. In this case, we are given the area and the length of one side of the room. We can use this information to find the width of the room, and then use the formula for the perimeter to find the final answer.

Step-by-Step Solution

Let's use System A to solve the problem.

Step 1: Find the Width of the Room

We are given the area (156 square feet) and the length (13 feet). We can use this information to find the width of the room.

156=13×w156 = 13 \times w

To solve for w, we can divide both sides of the equation by 13:

w=15613w = \frac{156}{13}

w=12w = 12

So, the width of the room is 12 feet.

Step 2: Find the Perimeter of the Room

Now that we have the width of the room, we can use the formula for the perimeter to find the final answer.

P=2×(L+W)P = 2 \times (L + W)

P=2×(13+12)P = 2 \times (13 + 12)

P=2×25P = 2 \times 25

P=50P = 50

So, the perimeter of the room is 50 feet.

Conclusion

In this article, we explored which system of equations can be used to solve the problem of finding the perimeter of a rectangular room given its area and the length of one side. We used System A to solve the problem, and found that the perimeter of the room is 50 feet.

Key Takeaways

  • Systems of equations are used to solve problems that involve multiple variables and relationships between them.
  • The formula for the area of a rectangle is Area = Length × Width.
  • The formula for the perimeter of a rectangle is P = 2 × (L + W).
  • To solve a problem involving a system of equations, we need to examine the given information and the formulas involved.
  • We can use the formula for the area to find the width of the room, and then use the formula for the perimeter to find the final answer.

Final Answer

Introduction

In our previous article, we explored which system of equations can be used to solve the problem of finding the perimeter of a rectangular room given its area and the length of one side. In this article, we will answer some frequently asked questions about systems of equations and provide additional guidance on how to use them to solve problems.

Q&A

Q: What is a system of equations?

A: A system of equations is a set of two or more equations that involve multiple variables and relationships between them. Systems of equations are used to solve problems that involve multiple variables and relationships between them.

Q: How do I know which system of equations to use?

A: To determine which system of equations to use, you need to examine the given information and the formulas involved. In this case, we are given the area and the length of one side of the room. We can use this information to find the width of the room, and then use the formula for the perimeter to find the final answer.

Q: What is the difference between System A and System B?

A: System A and System B are two different systems of equations that can be used to solve the problem. System A is based on the formula for the area of a rectangle and the formula for the perimeter of a rectangle. System B is also based on the formula for the area of a rectangle and the formula for the perimeter of a rectangle.

Q: How do I solve a system of equations?

A: To solve a system of equations, you need to follow these steps:

  1. Examine the given information and the formulas involved.
  2. Use the formula for the area to find the width of the room.
  3. Use the formula for the perimeter to find the final answer.

Q: What are some common mistakes to avoid when solving systems of equations?

A: Some common mistakes to avoid when solving systems of equations include:

  • Not examining the given information and the formulas involved.
  • Not using the correct formula for the area or perimeter.
  • Not following the correct steps to solve the system of equations.

Q: How can I practice solving systems of equations?

A: You can practice solving systems of equations by working through examples and exercises. You can also use online resources and practice tests to help you prepare.

Additional Tips and Resources

  • Make sure to read and understand the problem carefully before starting to solve it.
  • Use the correct formulas and equations to solve the problem.
  • Follow the correct steps to solve the system of equations.
  • Practice solving systems of equations regularly to build your skills and confidence.

Conclusion

In this article, we answered some frequently asked questions about systems of equations and provided additional guidance on how to use them to solve problems. We also discussed some common mistakes to avoid and provided tips and resources for practicing solving systems of equations.

Key Takeaways

  • Systems of equations are used to solve problems that involve multiple variables and relationships between them.
  • The formula for the area of a rectangle is Area = Length × Width.
  • The formula for the perimeter of a rectangle is P = 2 × (L + W).
  • To solve a system of equations, you need to examine the given information and the formulas involved.
  • You can practice solving systems of equations by working through examples and exercises.

Final Answer

The final answer is that systems of equations are a powerful tool for solving problems that involve multiple variables and relationships between them. By following the correct steps and using the correct formulas, you can solve systems of equations and find the final answer.