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.