The two triangles $A$ and $B$ are given as similar. Since they are similar, their corresponding sides are proportional.

Step-by-Step Solution:

• Triangle A has sides 18, 24, and 30.
• Triangle B has sides 20, and we need to find $x$.

We know that the corresponding sides of similar triangles have the same ratio. Let's use the sides given to set up a proportion.

The ratio of the sides between triangles A and B can be represented by:

$\frac{18}{20} = \frac{24}{x}$

To solve for $x$, we cross-multiply:

$18 \times x = 24 \times 20$

$18x = 480$

$x = \frac{480}{18}$

$x = 26.67$

After simplifying:

$x = 27 \quad (\text{approximately})$

Answer:

The correct answer is $x = 27$.

Would you like further details on any part of this solution, or have any questions?

Here are 5 related questions for further understanding:

1. How do we determine that two triangles are similar?
2. What properties do similar triangles share regarding their angles and sides?
3. How can the concept of similarity be applied to solve real-world problems?
4. What other methods are there to find the length of a side in a similar triangle?
5. How can trigonometry be used in relation to similar triangles?

Tip: When working with similar triangles, always ensure you are matching corresponding sides correctly to set up the right proportion.