Scale Factor is used to scale shapes in Different Dimensions be it 1, 2, or 3 dimensions. Letâ€™s explore what is scale factor through various solved problems, examples, and applications. It is used when we need to increase the size of a 2D shape. The size by which the shape is enlarged is called as its scale factor.
What is the Scale factor?
It is used when we need to increase the size of a 2D shape. The size by which the shape is enlarged is called as its scale factor.
Examples of Scale Factor
For example, thereâ€™s a rectangle with measurements 6 cm and 3 cm.
Both sides of the triangle will be doubled if we increase the scale factor for the original rectangle by 2. I.e By increasing the scale factor we mean to multiply the existing measurement of the rectangle by the given scale factor. Here, we have multiplied the original measurement of the triangle by 2.
Originally, the rectangleâ€™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.
Scale Factor Problems
Both sides will be triple if we increase the scale factor for the original rectangle by 3. I.e By increasing the scale factor we mean to multiply the existing measurement of the rectangle by the given scale factor. Here, we have multiplied the original measurement of the triangle by 3.
Originally, the rectangleâ€™s length was 6 cm and Breadth was 3 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.
Scale Factor of 2
The exampleÂ belowÂ 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?
Hint: Work Backwards, and divide the measurements of the new triangle by the original one to get the scale factor.
The answer is 2.
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.
Scale Factor Formula:
Dimensions of Larger rectangle x scale Factor = dimension of Smaller Square.
Step 1: 6 x scale factor = 3
Step 2: Scale factor = 3/6 (Divide each side by 6).
Step 3: Scale factor = Â½ =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.
Real-life Applications of Scale Factor
It is important to study real-life applications to understand the concept more clearly:
Because of various numbers getting multiplied or divided by a particular number to increase or decrease the given figure, Scale factor can be compared toÂ Ratios and Proportions.
- If thereâ€™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 let 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.
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Related Links | |
Construction of Similar Triangles | Common Multiples and Factors |
Factors and Multiples | Prime Factorization of HCF & LCM |