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How long is LK?
• |HI|= 100 units
• |HK|= 60 units
• |IJ|= 40 units

To determine the length of \( LK \), we can approach this by analyzing the geometry and given values in the image.

Given:
- \( |HI| = 100 \) units
- \( |HK| = 60 \) units
- \( |IJ| = 40 \) units

Looking at the figure, \( HIKJ \) forms a trapezoid, and \( L \) is the intersection point of the diagonal \( HK \) and the vertical segment connecting \( J \) to \( I \).

### Steps:
1. **Right triangle \( HIJ \)**: 
   - \( HI \) is the base, which is 100 units.
   - \( IJ \) is the height, which is 40 units.

2. **Right triangle \( HKL \)**:
   - Since \( LK \) is part of triangle \( HKL \) with known lengths of \( HK = 60 \) units and \( HJ = 100 \) units, and the point \( K \) seems vertically aligned with \( L \), we can use proportions or trigonometric relations to determine \( LK \).

   I will now calculate the length of \( LK \).The length of \( LK \) is 24 units.

Would you like further details or have any questions about this calculation?

Here are some related questions to consider:
1. How would you calculate the area of triangle \( HKL \)?
2. What is the area of trapezoid \( HIKJ \)?
3. Can we verify the similarity between triangles \( HKL \) and \( HIJ \)?
4. What is the slope of line \( HK \)?
5. How could you find the length of diagonal \( HJ \)?

**Tip:** When working with similar triangles, always check for proportional sides and equal angles to ensure similarity.

How long is LK? • |HI|= 100 units • |HK|= 60 units • |IJ|= 40 units

Learn how to determine the length of segment LK in a geometric trapezoid with given side lengths of |HI| = 100 units, |HK| = 60 units, and |IJ| = 40 units. This problem covers key geometric concepts such as triangle similarity and proportionality. Suitable for students in Grades 9-12.

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