Find The Perimeter Of A Tablet PC Where The Length Is $24.2 \text{ Mm}$ And The Width Is $x \text{ Cm}$.

by ADMIN 108 views

Introduction

In mathematics, the perimeter of a shape is the total length of its boundary. When it comes to a tablet PC, we can consider it as a rectangle with a fixed length and a variable width. In this article, we will explore how to find the perimeter of a tablet PC given its length and width.

Understanding the Problem

The problem states that the length of the tablet PC is $24.2 \text{ mm}$ and the width is x cmx \text{ cm}. To find the perimeter, we need to add up the lengths of all four sides of the rectangle. Since the length is given in millimeters and the width is given in centimeters, we need to convert the length to centimeters to ensure that both measurements are in the same unit.

Converting Units

To convert millimeters to centimeters, we can use the conversion factor: $1 \text{ cm} = 10 \text{ mm}$. Therefore, we can convert the length from millimeters to centimeters by dividing by 10.

24.2 mm=2.42 cm24.2 \text{ mm} = 2.42 \text{ cm}

Finding the Perimeter

Now that we have the length in centimeters, we can find the perimeter of the tablet PC. The formula for the perimeter of a rectangle is:

P=2l+2wP = 2l + 2w

where PP is the perimeter, ll is the length, and ww is the width.

Substituting the values, we get:

P=2(2.42)+2xP = 2(2.42) + 2x

P=4.84+2xP = 4.84 + 2x

Solving for x

Since we are given the perimeter, we can set up an equation and solve for xx. However, we are not given the perimeter, so we will leave the equation as is.

Graphical Representation

To visualize the relationship between the perimeter and the width, we can create a graph. We can plot the equation P=4.84+2xP = 4.84 + 2x and observe how the perimeter changes as the width increases.

Real-World Applications

Finding the perimeter of a tablet PC may seem like a trivial task, but it has real-world applications in various fields such as engineering, architecture, and design. For example, when designing a tablet PC, manufacturers need to consider the perimeter of the device to ensure that it fits comfortably in the user's hand.

Conclusion

In conclusion, finding the perimeter of a tablet PC involves converting units, applying the formula for the perimeter of a rectangle, and solving for the width. While this problem may seem simple, it has real-world applications and requires a thorough understanding of mathematical concepts.

Future Directions

In the future, we can explore more complex problems involving the perimeter of shapes with varying dimensions. We can also investigate the relationship between the perimeter and other mathematical concepts such as area and volume.

References

  • [1] "Perimeter of a Rectangle" by Math Open Reference
  • [2] "Converting Units" by Khan Academy

Glossary

  • Perimeter: The total length of the boundary of a shape.
  • Rectangle: A quadrilateral with four right angles.
  • Length: A measure of the distance between two points.
  • Width: A measure of the distance between two points in a direction perpendicular to the length.

Mathematical Formulas

  • Perimeter of a Rectangle: P=2l+2wP = 2l + 2w
  • Conversion Factor: 1 cm=10 mm1 \text{ cm} = 10 \text{ mm}

Introduction

In our previous article, we explored how to find the perimeter of a tablet PC given its length and width. In this article, we will answer some frequently asked questions related to this topic.

Q: What is the perimeter of a tablet PC?

A: The perimeter of a tablet PC is the total length of its boundary. It is calculated by adding up the lengths of all four sides of the rectangle.

Q: How do I convert millimeters to centimeters?

A: To convert millimeters to centimeters, you can use the conversion factor: $1 \text{ cm} = 10 \text{ mm}$. Therefore, you can convert millimeters to centimeters by dividing by 10.

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

A: The formula for the perimeter of a rectangle is:

P=2l+2wP = 2l + 2w

where PP is the perimeter, ll is the length, and ww is the width.

Q: How do I solve for x in the equation P = 4.84 + 2x?

A: To solve for x, you need to isolate x on one side of the equation. However, we are not given the perimeter, so we will leave the equation as is.

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

A: Finding the perimeter of a tablet PC has real-world applications in various fields such as engineering, architecture, and design. For example, when designing a tablet PC, manufacturers need to consider the perimeter of the device to ensure that it fits comfortably in the user's hand.

Q: Can I use this formula to find the perimeter of other shapes?

A: Yes, the formula for the perimeter of a rectangle can be used to find the perimeter of other shapes such as squares, triangles, and circles. However, the formula may need to be modified to accommodate the specific shape.

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

A: The perimeter of a shape is the total length of its boundary, while the area of a shape is the amount of space inside the shape. For example, the perimeter of a rectangle is the sum of the lengths of its four sides, while the area of a rectangle is the product of its length and width.

Q: Can I use a calculator to find the perimeter of a tablet PC?

A: Yes, you can use a calculator to find the perimeter of a tablet PC. Simply enter the values of the length and width, and the calculator will give you the perimeter.

Q: What are some common mistakes to avoid when finding the perimeter of a tablet PC?

A: Some common mistakes to avoid when finding the perimeter of a tablet PC include:

  • Not converting units correctly
  • Not using the correct formula for the perimeter of a rectangle
  • Not isolating x on one side of the equation
  • Not considering the real-world applications of finding the perimeter of a tablet PC

Conclusion

In conclusion, finding the perimeter of a tablet PC involves converting units, applying the formula for the perimeter of a rectangle, and solving for the width. We hope that this article has answered some of the frequently asked questions related to this topic.

Glossary

  • Perimeter: The total length of the boundary of a shape.
  • Rectangle: A quadrilateral with four right angles.
  • Length: A measure of the distance between two points.
  • Width: A measure of the distance between two points in a direction perpendicular to the length.
  • Area: The amount of space inside a shape.
  • Calculator: A device used to perform mathematical calculations.

Mathematical Formulas

  • Perimeter of a Rectangle: P=2l+2wP = 2l + 2w
  • Conversion Factor: 1 cm=10 mm1 \text{ cm} = 10 \text{ mm}