https://file.aiquickdraw.com/mathbot/file/1730431405008n1zdyprt.jpg

To solve for \( PR \) in this triangle problem, we can use the concept of similar triangles. Here’s the analysis step-by-step:

### Step-by-Step Solution

1. **Identify Similar Triangles**: 
   The two triangles \( \triangle PQK \) and \( \triangle PLR \) share the angle at \( P \). Also, they have pairs of corresponding sides that are proportional, making these triangles similar by the AA (Angle-Angle) criterion.

2. **Set Up the Proportion**:
   Since \( \triangle PQK \sim \triangle PLR \), we can set up the following proportion based on the sides:
   \[
   \frac{PQ}{PL} = \frac{PK}{PR}
   \]
   
3. **Substitute Known Values**:
   From the diagram:
   - \( PQ = 5 \)
   - \( PL = 12 \)
   - \( QR = 18 \) (Since we are given the full segment \( PR \) and \( PL \) is part of it)
   
   Using these values, rewrite the proportion as:
   \[
   \frac{5}{12} = \frac{12}{PR}
   \]

4. **Cross Multiply to Solve for \( PR \)**:
   \[
   5 \cdot PR = 12 \cdot

Find the missing length indicated. Find PR.

Learn how to find the missing length PR in a triangle using similar triangles and proportions. This geometry problem involves setting up and solving proportions based on the AA similarity criterion. Suitable for students in Grades 9-10.

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