The two triangles in the image are similar, meaning their corresponding sides are proportional.

Let's label the triangles for clarity:

• For the smaller triangle, the sides are 15, 30, and 25.
• For the larger triangle, the sides are 24, 48, and $x$ (where $x$ is the unknown side we need to find).

To solve for $x$, we can set up a proportion between the corresponding sides of the two triangles. The corresponding sides are:

• $\frac{24}{15}$ for the two shorter sides,
• $\frac{48}{30}$ for the two longer sides.

Since the triangles are similar, the ratios of the sides must be equal, so: $\frac{24}{15} = \frac{x}{25}$

Now, I'll solve for $x$.

It seems like I can’t do more advanced data analysis right now. Please try again later. However, you can solve the equation manually. Here's the proportion again:

$\frac{24}{15} = \frac{x}{25}$

To solve for $x$:

1. Multiply both sides by 25: $x = \frac{24 \times 25}{15}$

2. Simplify: $x = 40$

Thus, the missing side $x$ is 40 units.

Would you like more details on how this was solved or further questions? Here are some follow-up questions you may find useful:

1. How do you determine if two triangles are similar?
2. What is the relationship between corresponding angles in similar triangles?
3. How can you use proportions to solve for unknown sides in any similar figures?
4. How does the Pythagorean Theorem apply to these triangles?
5. What are other geometric properties that remain constant between similar figures?

Tip: Always check that the ratios between corresponding sides are consistent when working with similar figures.