To determine the scale factor between the two triangles in the image:

We are given two triangles:

1. The left triangle has side lengths of 7 and 7.
2. The right triangle has side lengths of $\frac{7}{3}$ and $\frac{7}{3}$.

Finding the scale factor:

The scale factor is the ratio of the corresponding sides of the two triangles. Let's compare the corresponding sides:

$\text{Scale factor} = \frac{\text{Side length of the right triangle}}{\text{Side length of the left triangle}}$

For the sides with lengths 7 on the left triangle and $\frac{7}{3}$ on the right triangle:

$\text{Scale factor} = \frac{\frac{7}{3}}{7} = \frac{7}{3} \times \frac{1}{7} = \frac{1}{3}$

Thus, the scale factor is $\frac{1}{3}$, meaning the right triangle is scaled down by a factor of 1/3 compared to the left triangle.

Would you like any further details or have any other questions?

Related questions:

1. What is the definition of a scale factor in geometry?
2. How do you find the scale factor between two shapes that are not triangles?
3. Can the scale factor ever be negative? If so, what would it mean?
4. How does the scale factor affect the area of a shape?
5. How would you solve if one of the sides was unknown?

Tip: When comparing similar triangles, always check if their angles are congruent before determining the scale factor based on side lengths.