To find the value of $x$ given that the triangles are similar, we can set up a proportion using the corresponding sides of the similar triangles.

Given triangles:

• Triangle 1: sides are 96, 28, and $6x + 28$
• Triangle 2: sides are 24, 7, and 25

The corresponding sides are in proportion because the triangles are similar.

We can use the corresponding sides to set up a proportion: $\frac{96}{24} = \frac{28}{7} = \frac{6x + 28}{25}$

First, simplify the fractions: $\frac{96}{24} = 4$ $\frac{28}{7} = 4$

Thus, the proportion is: $4 = \frac{6x + 28}{25}$

Now, solve for $x$: $4 \cdot 25 = 6x + 28$ $100 = 6x + 28$ $100 - 28 = 6x$ $72 = 6x$ $x = \frac{72}{6}$ $x = 12$

So, the value of $x$ is 12.

Would you like more details on this explanation, or do you have any questions?

Here are some more questions you might find interesting:

1. How do you determine the scale factor between similar triangles?
2. Can you explain how to use the Pythagorean Theorem to find missing sides in a right triangle?
3. What are some properties of similar triangles?
4. How do you solve proportions involving variables?
5. What are some real-life applications of triangle similarity and proportions?

Tip: When working with similar triangles, always identify the corresponding sides and set up proportions to solve for unknown variables.