Search Model Trained on March 2025 | Vector Size: 1024 | Vocab Size: 153496
Okay, let's break down how to calculate the scale factor between two similar figures given their side lengths.
Understanding Similarity
Similar figures are figures that have the same shape but can be different sizes. This means their corresponding angles are equal, and their corresponding sides are proportional.
The Scale Factor
The scale factor is a number that represents how much larger or smaller one figure is compared to the other. It's defined as the ratio of the corresponding side lengths of the larger figure to the corresponding side lengths of the smaller figure.
How to Calculate It
Identify Corresponding Sides: First, you need to determine which sides in the two figures correspond to each other. For example, if you have a small triangle and a large triangle, the shortest side of the small triangle corresponds to the shortest side of the large triangle, the next shortest side corresponds to the next shortest side, and so on.
Calculate the Ratio: Divide the length of a side in the larger figure by the length of the corresponding side in the smaller figure.
Scale Factor = (Length of side in larger figure) / (Length of corresponding side in smaller figure)
Simplify (if possible): Reduce the fraction you calculated to its simplest form. This will give you the scale factor as a whole number, a fraction, or a decimal.
Example
Let's say you have two similar rectangles:
- Rectangle A: Length = 6 cm, Width = 4 cm
- Rectangle B: Length = 9 cm, Width = 6 cm
Corresponding Sides:
- Rectangle A's length corresponds to Rectangle B's length.
- Rectangle A's width corresponds to Rectangle B's width.
Calculate the Ratio:
- Scale Factor = (Length of Rectangle B) / (Length of Rectangle A) = 9 cm / 6 cm = 3/2 = 1.5
Simplify: The scale factor is 1.5. This means that Rectangle B is 1.5 times larger than Rectangle A. Or, Rectangle A is 2/3 the size of Rectangle B.
Important Notes:
- Larger Figure First: When calculating the scale factor, always put the larger figure's side length in the numerator.
- Units: Make sure the units are the same for both side lengths before calculating the ratio.
- Scale Factor > 1: A scale factor greater than 1 indicates that the larger figure is bigger.
- Scale Factor < 1: A scale factor less than 1 indicates that the smaller figure is bigger.
In summary, the scale factor is simply the ratio of corresponding side lengths, and it tells you how much larger or smaller one figure is relative to the other.
Do you want me to work through another example, or would you like me to explain a specific aspect of this in more detail (like how to determine corresponding sides in different types of figures)?
More questions on topic
What is the definition of similar figures?
How is the scale factor defined?
What steps are involved in calculating the scale factor between two similar figures?
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