Finding the Forgotten Length

Oct 13, 2025 by talynt.org 8 views

Introduction

In mathematics, scale factors and ratio tables are essential tools for understanding how shapes change when they are enlarged or reduced. A scale factor is a number that represents the ratio of the size of a shape after enlargement or reduction to its original size. Ratio tables are used to show the original dimensions of a shape and the dimensions when changed by a scale factor. In this article, we will explore how Fabian used a ratio table to show the original dimensions of a rectangle and the dimensions when changed by a scale factor, and how he forgot to enter the length of the new rectangle.

What is a Scale Factor?

A scale factor is a number that represents the ratio of the size of a shape after enlargement or reduction to its original size. It is used to describe how much a shape is enlarged or reduced. For example, if a shape is enlarged by a scale factor of 2, it means that the new shape is twice as large as the original shape. On the other hand, if a shape is reduced by a scale factor of 0.5, it means that the new shape is half as large as the original shape.

What is a Ratio Table?

A ratio table is a table that shows the original dimensions of a shape and the dimensions when changed by a scale factor. It is used to compare the original dimensions of a shape with its new dimensions after enlargement or reduction. A ratio table typically consists of two columns: one for the original dimensions and one for the new dimensions. The ratio of the new dimensions to the original dimensions is shown in the table.

Fabian's Ratio Table

Fabian used a ratio table to show the original dimensions of a rectangle and the dimensions when changed by a scale factor. The ratio table is shown below:

Scale Factor	Original Length	Original Width	New Length	New Width
1	10	5	10	5
2.5

The Forgotten Length

As we can see from the ratio table, Fabian forgot to enter the length of the new rectangle. This means that we do not know the new length of the rectangle when it is enlarged by a scale factor of 2.5.

Finding the Forgotten Length

To find the forgotten length, we need to use the scale factor to calculate the new length. Since the scale factor is 2.5, we can multiply the original length by 2.5 to get the new length.

Calculating the New Length

Let's calculate the new length using the scale factor.

New Length = Original Length x Scale Factor = 10 x 2.5 = 25

Conclusion

In conclusion, Fabian used a ratio table to show the original dimensions of a rectangle and the dimensions when changed by a scale factor. However, he forgot to enter the length of the new rectangle. By using the scale factor, we were able to calculate the forgotten length and find the new length of the rectangle.

Real-World Applications

Scale factors and ratio tables have many real-world applications. For example, architects use scale factors to design buildings and bridges. Engineers use scale factors to design machines and mechanisms. Artists use scale factors to create sculptures and paintings.

Tips and Tricks

Here are some tips and tricks for working with scale factors and ratio tables:

Always check the scale factor before using it to calculate new dimensions.
Make sure to enter all the necessary information in the ratio table.
Use the scale factor to calculate new dimensions, rather than trying to estimate them.
Practice using scale factors and ratio tables to become more confident and proficient.

Common Mistakes

Here are some common mistakes to avoid when working with scale factors and ratio tables:

Forgetting to enter necessary information in the ratio table.
Using the wrong scale factor to calculate new dimensions.
Not checking the scale factor before using it to calculate new dimensions.
Not practicing using scale factors and ratio tables to become more confident and proficient.

Conclusion

Introduction

In our previous article, we explored how Fabian used a ratio table to show the original dimensions of a rectangle and the dimensions when changed by a scale factor. However, he forgot to enter the length of the new rectangle. In this article, we will answer some frequently asked questions about scale factors and ratio tables.

Q: What is a scale factor?

A: A scale factor is a number that represents the ratio of the size of a shape after enlargement or reduction to its original size. It is used to describe how much a shape is enlarged or reduced.

Q: What is a ratio table?

A: A ratio table is a table that shows the original dimensions of a shape and the dimensions when changed by a scale factor. It is used to compare the original dimensions of a shape with its new dimensions after enlargement or reduction.

Q: How do I use a scale factor to calculate new dimensions?

A: To use a scale factor to calculate new dimensions, you need to multiply the original dimensions by the scale factor. For example, if the original length is 10 and the scale factor is 2, the new length would be 20.

Q: What if I forget to enter the length of the new rectangle?

A: If you forget to enter the length of the new rectangle, you can use the scale factor to calculate the new length. Simply multiply the original length by the scale factor to get the new length.

Q: Can I use a scale factor to reduce a shape?

A: Yes, you can use a scale factor to reduce a shape. To reduce a shape, you need to use a scale factor that is less than 1. For example, if you want to reduce a shape by half, you would use a scale factor of 0.5.

Q: How do I know which scale factor to use?

A: The scale factor you use will depend on the problem you are trying to solve. If you are trying to enlarge a shape, you will use a scale factor that is greater than 1. If you are trying to reduce a shape, you will use a scale factor that is less than 1.

Q: Can I use a ratio table to compare the dimensions of two shapes?

A: Yes, you can use a ratio table to compare the dimensions of two shapes. Simply enter the original dimensions of both shapes into the ratio table and compare the new dimensions.

Q: What are some common mistakes to avoid when working with scale factors and ratio tables?

A: Some common mistakes to avoid when working with scale factors and ratio tables include:

Forgetting to enter necessary information in the ratio table.
Using the wrong scale factor to calculate new dimensions.
Not checking the scale factor before using it to calculate new dimensions.
Not practicing using scale factors and ratio tables to become more confident and proficient.

Q: How can I practice using scale factors and ratio tables?

A: You can practice using scale factors and ratio tables by working through problems and exercises. You can also use online resources and worksheets to help you practice.

Conclusion

In conclusion, scale factors and ratio tables are essential tools for understanding how shapes change when they are enlarged or reduced. By using a ratio table and a scale factor, we can calculate new dimensions and compare the dimensions of two shapes. With practice and patience, we can become more confident and proficient in using scale factors and ratio tables.

Additional Resources

Online resources and worksheets for practicing scale factors and ratio tables.
Video tutorials and explanations for understanding scale factors and ratio tables.
Practice problems and exercises for working through scale factors and ratio tables.

Common Terms

Scale factor: A number that represents the ratio of the size of a shape after enlargement or reduction to its original size.
Ratio table: A table that shows the original dimensions of a shape and the dimensions when changed by a scale factor.
New dimensions: The dimensions of a shape after enlargement or reduction.
Original dimensions: The dimensions of a shape before enlargement or reduction.