Use a ruler or other measuring tool

Oct 13, 2025 by miodeya.com 12 views

Introduction

Scaling is a fundamental concept in mathematics that involves changing the size of a shape or object while maintaining its proportions. In this article, we will explore the concept of scaling a square picture using a photocopier. We will calculate the side length of the second copy of the picture after it has been scaled by 60% twice.

Scaling a Square Picture

A square picture with a side length of 30 cm is scaled by 60% on a photocopier. This means that the new side length of the picture will be 60% of the original side length.

Calculating the Side Length of the First Copy

To calculate the side length of the first copy, we can use the following formula:

Side length of the first copy = (60% of the original side length) = (0.6) × (30 cm) = 18 cm

So, the side length of the first copy of the picture is 18 cm.

Scaling the First Copy

The first copy of the picture is then scaled by 60% again. This means that the new side length of the picture will be 60% of the side length of the first copy.

Calculating the Side Length of the Second Copy

To calculate the side length of the second copy, we can use the following formula:

Side length of the second copy = (60% of the side length of the first copy) = (0.6) × (18 cm) = 10.8 cm

So, the side length of the second copy of the picture is 10.8 cm.

Conclusion

In this article, we have explored the concept of scaling a square picture using a photocopier. We have calculated the side length of the second copy of the picture after it has been scaled by 60% twice. The side length of the second copy is 10.8 cm.

Real-World Applications

Scaling is a fundamental concept in mathematics that has many real-world applications. Some examples include:

Architecture: Architects use scaling to design buildings and other structures that are proportional to the surrounding environment.
Graphic Design: Graphic designers use scaling to create images and graphics that are proportional to the surrounding text and other elements.
Engineering: Engineers use scaling to design machines and other devices that are proportional to the surrounding environment.

Tips and Tricks

Use a calculator: When working with percentages, it can be helpful to use a calculator to ensure accuracy.
Check your units: Make sure to check your units when working with measurements to ensure that they are consistent.
Use a ruler or other measuring tool: When working with measurements, it can be helpful to use a ruler or other measuring tool to ensure accuracy.

Frequently Asked Questions

What is scaling? Scaling is a fundamental concept in mathematics that involves changing the size of a shape or object while maintaining its proportions.
How do I calculate the side length of a scaled shape? To calculate the side length of a scaled shape, you can use the following formula: Side length of the scaled shape = (percentage of the original side length) × (original side length).
What are some real-world applications of scaling? Some examples of real-world applications of scaling include architecture, graphic design, and engineering.

Glossary

Scaling: A fundamental concept in mathematics that involves changing the size of a shape or object while maintaining its proportions.
Percentage: A number that represents a proportion of a whole.
Side length: The length of one side of a shape or object.

References

[1] "Scaling." Math Open Reference, mathopenref.com/scaling.html.
[2] "Percentages." Khan Academy, khanacademy.org/math/percentages.
[3] "Side Length." Math Is Fun, mathisfun.com/geometry/side-length.html.
Mathematics: Scaling a Square Picture Q&A =====================================

Introduction

In our previous article, we explored the concept of scaling a square picture using a photocopier. We calculated the side length of the second copy of the picture after it had been scaled by 60% twice. In this article, we will answer some frequently asked questions about scaling a square picture.

Q&A

Q: What is scaling?

A: Scaling is a fundamental concept in mathematics that involves changing the size of a shape or object while maintaining its proportions.

Q: How do I calculate the side length of a scaled shape?

A: To calculate the side length of a scaled shape, you can use the following formula:

Side length of the scaled shape = (percentage of the original side length) × (original side length)

Q: What are some real-world applications of scaling?

A: Some examples of real-world applications of scaling include:

Architecture: Architects use scaling to design buildings and other structures that are proportional to the surrounding environment.
Graphic Design: Graphic designers use scaling to create images and graphics that are proportional to the surrounding text and other elements.
Engineering: Engineers use scaling to design machines and other devices that are proportional to the surrounding environment.

Q: How do I calculate the side length of a shape that has been scaled multiple times?

A: To calculate the side length of a shape that has been scaled multiple times, you can use the following formula:

Side length of the scaled shape = (percentage of the original side length) × (percentage of the previous side length) × (original side length)

Q: What is the difference between scaling and resizing?

A: Scaling involves changing the size of a shape or object while maintaining its proportions, whereas resizing involves changing the size of a shape or object without maintaining its proportions.

Q: How do I use scaling in real-world applications?

A: To use scaling in real-world applications, you can follow these steps:

Identify the shape or object: Identify the shape or object that you want to scale.
Determine the scaling factor: Determine the scaling factor that you want to use.
Apply the scaling factor: Apply the scaling factor to the shape or object.
Check the proportions: Check the proportions of the scaled shape or object to ensure that they are maintained.