To find the scale factor between the two triangles, we can compare the lengths of corresponding sides in the "preimage" triangle (smaller triangle) and the "image" triangle (larger triangle).

Solution

Let's calculate the scale factor using a pair of corresponding side lengths.

1. Identify corresponding sides:

   • $AB$ in the preimage corresponds to $A'B'$ in the image.
   • $AC$ in the preimage corresponds to $A'C'$ in the image.
   • $AD$ in the preimage corresponds to $A'D'$ in the image.

2. Calculate the scale factor: Choose one set of corresponding sides and divide the length of the image side by the length of the preimage side.

   • For sides $AB$ and $A'B'$: $\text{Scale Factor} = \frac{A'B'}{AB} = \frac{4.9}{3} \approx 1.63$

3. Verify with another pair:

   • For sides $AD$ and $A'D'$: $\text{Scale Factor} = \frac{A'D'}{AD} = \frac{11.6}{4.6} \approx 2.52$

It appears that there might be an inconsistency between the measurements for different side ratios. However, based on the exact measurements shown, the initial calculated scale factor of approximately 1.63 applies only to the pair $AB$ and $A'B'$. Please check if the diagram accurately represents the consistent scale across all sides, or clarify the problem statement.

Would you like further assistance with details or another approach to verifying consistency?

Related Questions

1. How do you verify if two triangles are similar?
2. What is the importance of maintaining a consistent scale factor across all sides in similar figures?
3. How can you calculate the area ratio based on the scale factor?
4. What happens to the perimeter of a shape when it’s scaled by a certain factor?
5. How do you determine the scale factor if only some side lengths are known?

Tip: Always double-check all pairs of corresponding sides to confirm consistency in scale, especially if multiple sides are labeled.