Scale Factor Examples
Example 1: A rectangle undergoes a reduction with a scale factor of 0.5, resulting in new dimensions of 4 meters by 6 meters. Determine the dimensions of the original rectangle before the reduction.
Solution:
Given that the rectangle underwent a reduction with a scale factor of 0.5, and the new dimensions are 4 meters by 6 meters, we can find the original dimensions using the formula:
Original Dimention = New Dimension / Scale Factor
Original Length = 4m/0.5
⇒ Original Length = 8 meters
Original Width = 6m/0.5
⇒ Original Width = 12 meters
∴ The dimensions of the original rectangle before the reduction were 8 meters by 12 meters.
Example 2: A map has a scale factor of 1 inch to 5 miles. If two cities are 30 miles apart, what is the distance between them on the map?
Solution:
Given the scale factor of 1 inch to 5 miles, we can set up a proportion to find the distance on the map.
Let (x) be the distance on the map (in inches).
1 inch/5 miles = x/30 miles
Cross-multiplying:
⇒ 5x = 30
Dividing both sides by 5:
x = 6
So, the distance between the two cities on the map is 6 inches.
Scale Factor | Definition, Formula, Meaning, Types, and Examples
A scale factor represents the ratio of corresponding sides between two similar shapes. For example, a scale factor of 3 means that the new shape is three times larger than the original. Conversely, a scale factor of one-third indicates that the new shape is one-third the size of the original.
Scale Factor is a numerical representation that describes the proportional relationship between the corresponding dimensions of an original figure and its resized version. It quantifies the degree of enlargement or reduction in size during geometric transformations, aiding in precise adjustments.
In this article, we have covered the meaning of scale factor, its formula, types of scale factor — upscale and downscale, methods to find scale factor in different geometry shapes and applications of the scale factor.
Table of Content
- What is the Scale Factor?
- Scale Factor Meaning
- Scale Factor Symbol
- Scale Factor Formula
- Types of Scale Factor
- Up Scale or Enlargement Scale Factor
- Down Scale or Reduction Scale Factor
- How to Find the Scale Factor
- Scale Factor of Triangle
- Scale Factor of a Circle
- Scale Factor of a Rectangle
- Scale Factor of Other Figures
- Applications of Scale Factor
- Scale Factor Examples
- Praactice Questions on Scale Factor
- Summary – Scale Factor