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This problem involves two similar triangles based on their corresponding angles (75°, 55°, and the third angle). Since the triangles are similar, we can use the proportionality of corresponding sides to find the length of side \( PR \).

Given:

- In the larger triangle \( \triangle ABC \):
  - \( AB = 20 \)
  - \( AC = 24 \)

- In the smaller triangle \( \triangle PQR \):
  - \( PQ = 5 \)
  - We need to find \( PR = x \).

Since the triangles are similar, we can set up the proportion:
\[
\frac{AB}{PQ} = \frac{AC}{PR}
\]

Substitute the given values:
\[
\frac{20}{5} = \frac{24}{x}
\]

Now solve for \( x \):
\[
4 = \frac{24}{x}
\]
\[
x = \frac{24}{4} = 6
\]

Thus, the length of \( PR \) is \( 6 \), so the correct answer is **D. 6**.

Would you like more details or have any questions?

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Here are 5 related questions to expand on this topic:
1. How do we know that the two triangles are similar?
2. What other methods can be used to determine the similarity of triangles?
3. What is the ratio of the areas of two similar triangles?
4. Can we solve this problem using trigonometry instead of proportions?
5. What happens to the angles of a triangle when the sides are scaled proportionally?

**Tip:** Always check if the given triangles share common angles, as this can often indicate triangle similarity, which allows you to use proportions for solving side lengths.

What is the length of PR in the given similar triangles?

Solve for the length of PR in two similar triangles using the properties of proportionality. This problem covers key geometric concepts related to similar triangles and proportional sides, suitable for students in Grades 9-10.

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