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- Mathematics

## How to Find Scale Factor

Last Updated: September 15, 2022 References

## Finding the Scale Factor of Similar Figures

## Finding a Similar Figure Using the Scale Factor

## Completing Sample Problems

## Finding the Scale Factor in Chemistry

- The molar mass of H2O is 18.0152 g/mol.
- Find the scaling factor by dividing the molar mass of the compound by the molar mass of the empirical formula:
- Scaling factor = 54.05 / 18.0152 = 3

## Community Q&A

## Video . By using this service, some information may be shared with YouTube.

## You Might Also Like

- ↑ https://www.cuemath.com/geometry/scale-factor/
- ↑ http://www.mathsisfun.com/geometry/similar.html
- ↑ http://www.virtualnerd.com/pre-algebra/ratios-proportions/similar-figures-indirect-measurement/similar-figures/find-scale-factor-similar-figures
- ↑ Mario Banuelos, PhD. Assistant Professor of Mathematics. Expert Interview. 19 January 2021.
- ↑ http://www.virtualnerd.com/pre-algebra/ratios-proportions/missing-measurements-similar-figures-scale-factor.php
- ↑ http://www.vias.org/physics/bk1_03_02b.html

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## Scale Factor

## Scale Factor of Triangle

## What is the Scale factor

Hence, we can consider K as a constant of proportionality here.

The scale factor can also be better understood by Basic Proportionality Theorem .

## Scale Factor Formula

The formula for scale factor is given by:

Dimensions of Original Shape x scale Factor = Dimension of new shape

Scale factor = Dimension of New Shape/Dimension of Original Shape

Step 2: Scale factor = 3/6 (Divide each side by 6).

Step 3: Scale factor = ½ =1:2(Simplified).

Hence, the scale factor from the larger Square to the smaller square is 1:2.

The scale factor can be used with various different shapes too.

## Scale Factor Problem

For example, there’s a rectangle with measurements 6 cm and 3 cm.

Originally, the rectangle’s length was 6 cm and Breadth was 3 cm.

After increasing its scale factor by 2, the length is 12 cm and Breadth is 6 cm.

After increasing its scale factor by 3, the length is 18 cm and Breadth is 9 cm.

## How to find the scale factor of Enlargement

Problem 1: Increase the scale factor of the given Rectangle by 4.

Hint: Multiply the given measurements by 4.

Solution: Given Length of original rectangle = 4cm

Width or breadth of given rectangle = 2cm

Thus, we need to multiply the dimensions of given rectangle by 4.

Therefore, the dimensions of new rectangle or enlarged rectangle is given by:

## Scale Factor of 2

The example below will help you to understand the concept of scale factor of 2.

Problem 2: Look at square Q. What scale factor has square P increased by?

Solution : Divide the length of one side of the larger square by the scale factor.

We will get the length of the corresponding side of the smaller square.

## Real-life Applications of Scale Factor

It is important to study real-life applications to understand the concept more clearly:

- If there’s a larger group of people than expected at a party at your home. You need to increase the ingredients of the food items by multiplying each one by the same number to feed them all. Example, If there are 4 people extra than you expected and one person needs 2 pizza slices, then you need to make 8 more pizza slices to feed them all.
- Similarly, the Scale factor is used to find a particular percentage increase or to calculate the percentage of an amount.
- It also lets us work out the ratio and proportion of various groups, using the times’ table knowledge.
- To transform Size: In this, the ratio of expressing how much to be magnified can be worked out.
- Scale Drawing: It is the ratio of measuring the drawing compared to the original figure given.
- To compare 2 Similar geometric figures: When we compare two similar geometric figures by the scale factor, it gives the ratio of the lengths of the corresponding sides.

Put your understanding of this concept to test by answering a few MCQs. Click ‘Start Quiz’ to begin!

Visit BYJU’S for all Maths related queries and study materials

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## Scale Factor — Definition, Formula & How To Find

## Scale factor definition

A scale factor ratio can be expressed as a fraction, 1 2 \frac{1}{2} 2 1 , or a colon, 1:2 .

## How to find scale factor

To find the scale factor, you first decide which direction you are scaling:

Scale Up (smaller to larger) = larger measurement / smaller measurement

Scale Down (larger to smaller) = smaller measurement / larger measurement

The scale factor for scaling up is a ratio greater than 1 .

The scale factor for scaling down is a ratio less than 1 .

## Finding scale factor of similar figures

Here are two similar triangles. What is the scale factor used to create the second, larger figure?

Since we are scaling up , we divide the larger number by the smaller number:

Because we are scaling down, we divide corresponding side lengths (smaller number by larger number):

If we have the big right triangle and want to scale it down to make the smaller one, we write this:

## Scale factor in geometry

## How to reduce a shape by a scale factor?

Suppose you are given a figure and told to reduce it by 25% . Think in steps:

Are you making a larger or smaller dilation?

You are shrinking the original, so your scale factor will be less than a whole number.

Next, measure (or read) any side of the figure and do some math.

Multiply 16 × 3 4 \frac{3}{4} 4 3 :

The height of our smaller rectangle must be 4.5 inches .

## How to make a scale model

## Scale factor examples

What is the definition of scale factor?

How do you find the scale factor of similar figures?

What information does a scale factor give?

Please do not peek ahead until you try your best to find the answers.

A scale factor gives the ratio of the representation to the actual object.

## How to use scale factor

Draw similar figures in geometry

Draw scale blueprints of architecture and machinery

## How Do You Solve a Scale Model Problem Using a Scale Factor?

## Background Tutorials

## What's a Numerator and What's A Denominator?

## How Do You Reduce A Fraction?

## Proportion Definitions

## What's a Ratio?

## Rates and Dimensional Analysis

## How Do You Use Dimensional Analysis to Convert Units on One Part of a Rate?

## Similar Figures and Indirect Measurement

## What is a Scale Drawing?

## How Do You Find Missing Measurements of Similar Figures Using a Scale Factor?

## How Do You Find a Scale Factor in Similar Figures?

## Further Exploration

## How Do You Solve a Word Problem Using a Proportion?

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## Scale Factor of Similar Figures Worksheets

Enlarge or Reduce - Real Life Objects

Scale Factor Word Problems - Level 1

Scale Factor Word Problems - Level 2

Find the Missing Side - Level 1

Find the Missing Side - Level 2

Scale Factor Worksheets - Area and Perimeter

Scale Factor Worksheets - Surface Area and Volume

Dilation Worksheets - Center at the Origin

Dilation Worksheets - Center not at the Origin

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## IMAGES

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## COMMENTS

to Find Scale FactorUse the scale factor to answer this problem. Multiply the height of Rectangle ABCD by the scale factor. This will give you the height of Rectangle EFGH: 3 × 2.5 = 7. Multiply the width of Rectangle ABCD by the scale factor. This will give you the width of Rectangle EFGH: 8 × 2.5 = 20... Multiply the ...

Scale FactorHow to find the scale factor of Enlargement Problem 1: Increase the scale factor of the given Rectangle by 4. Hint: Multiply the given measurements by 4. Solution: Given Length of original rectangle = 4cm Width or breadth of given rectangle = 2cm Now as per the given question, we need to increase the size of the given triangle by scale factor of 4.

Scale FactorTo find the scale factor, you first decide which direction you are scaling: Scale Up (smaller to larger) = larger measurement / smaller measurement. Scale Down (larger to smaller) = smaller measurement / larger measurement.

SolveaScaleModelProblemUsing aScale Factor?You could use a scale factor to solve! In this tutorial, learn how to create a ratio of corresponding sides with known length and use the ratio to find the scale factor. Then, write an equation using the scale factor to find your missing measurement! How Do You Find a Scale Factor in Similar Figures? Have similar figures?

Solving a scale drawingwordproblem(video)Solving a scale drawing word problem CCSS.Math: 7.G.A.1 Google Classroom About Transcript See how we solve a word problem by using a scale drawing and finding the scale factor. Created by Sal Khan. Sort by: Top Voted Questions Tips & Thanks shillpak28 7 years ago at 3:47

Scale FactorWorksheetsScale Factor - MCQ Put on your thinking caps to find the answer that best fits the problem in these printable MCQ worksheets. Determine the actual length, find the original or scaled copy of a model, identify the scale factor of similar figures and more. Scale Factor Word Problems - Level 1

How to SolveWordProblemsInvolvingScaleDrawingsStep 1: Find a common length whose measurements are given both on the drawing or model, and in real life. Step 2: If necessary, set these two measurements equal to each other using on-the-drawing (OTD), and in-real-life (IRL)... Step 3: Divide both sides of the equality by the number of ...

SolvingForScale Factora friend and I's math project

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Scale Model ProblemsSolving One Variable Equations Scale Model Problems Mr. T's Math Videos 6.53K subscribers Subscribe 163 33K views 13 years ago 2 problems showing how solve …