# Find the scale factor of triangle ABC to triangle DEF

• MHB
• masters1
In summary, the scale factor of triangle ABC to triangle DEF is 3/2. This is different from the scale ratio, which is 2/3, and the answer to the question is D, 3/2.
masters1
Triangles ABC and DEF are similar.

Triangle ABC has a perimeter of 16cm.

Triangle DEF has side of 6cm, 8cm and 10cm.

What is the scale factor of triangle ABC to triangle DEF?

A. 1/2
B. 1/3
C. 2/3
D. 3/2
E. 2/1

I concluded the answer is D. Am I correct?

What is the scale factor of triangle ABC to triangle DEF?

perimeter of ABC : perimeter of DEF = 16:24 = 2:3

There is a difference between the "scale factor of triangle ABC to triangle DEF" and the "scale factor of triangle DEF to triangle ABC". You found the wrong one! Since ABC is smaller than DEF, the scale factor is less than 1.

Then, is this textbook example incorrect?

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The dilation scale factor, which is a transformation, of triangle ABC to triangle DEF is 3/2

The scale ratio, like a map's scale, of triangle ABC to triangle DEF is 2/3

Sorry for the confusion.

skeeter said:
The dilation scale factor, which is a transformation, of triangle ABC to triangle DEF is 3/2

The scale ratio, like a map's scale, of triangle ABC to triangle DEF is 2/3

Sorry for the confusion.

So, the question asked about "scale factor", not ratio of any kind. Is the answer, in fact, "D", which is 3/2?

## 1. What is a scale factor?

A scale factor is a number that represents the ratio of corresponding sides of two similar figures. It is used to scale, or resize, one figure to match the size of the other.

## 2. How do you find the scale factor of two triangles?

To find the scale factor of two triangles, you need to compare the lengths of their corresponding sides. Divide the length of one side of the larger triangle by the length of the corresponding side of the smaller triangle. The resulting number is the scale factor.

## 3. What is the relationship between the scale factor and the similarity of two triangles?

The scale factor is directly related to the similarity of two triangles. If the scale factor is equal to 1, the triangles are congruent and have the same size and shape. If the scale factor is greater than 1, the triangles are similar but not congruent, and if the scale factor is less than 1, the triangles are also similar but smaller in size.

## 4. Can the scale factor be negative?

No, the scale factor cannot be negative. It represents a ratio and must be a positive number.

## 5. How is the scale factor used in real-life applications?

The scale factor is used in various fields, such as architecture, engineering, and cartography, to create accurate scaled models or drawings of objects or structures. It is also used in map-making to represent real-life distances on a smaller scale.

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