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To solve for the length \( LN \) using the Pythagorean Theorem, we can break this into two steps because two right triangles are involved.

### Given:
- Triangle \( KLM \) is a right triangle with:
  - \( KL = 25 \) (hypotenuse)
  - \( KM = 17 \) (one leg)
  - We need to find \( LM \) (the other leg).

- Triangle \( LMN \) is another right triangle with:
  - \( LM \) (hypotenuse of this triangle) will be calculated in the first part.
  - \( MN = 8 \) (one leg of the second triangle)
  - We need to find \( LN \) (the other leg).

#### Step 1: Find \( LM \) using triangle \( KLM \)

Apply the Pythagorean theorem to triangle \( KLM \):
\[
KL^2 = KM^2 + LM^2
\]
\[
25^2 = 17^2 + LM^2
\]
\[
625 = 289 + LM^2
\]
\[
LM^2 = 625 - 289 = 336
\]
\[
LM = \sqrt{336} \approx 18.33
\]

#### Step 2: Find \( LN \) using triangle \( LMN \)

Now, apply the Pythagorean theorem to triangle \( LMN \):
\[
LM^2 = LN^2 + MN^2
\]
\[
18.33^2 = LN^2 + 8^2
\]
\[
336 = LN^2 + 64
\]
\[
LN^2 = 336 - 64 = 272
\]
\[
LN = \sqrt{272} \approx 16.49
\]

### Final Answer:
The length of \( LN \) is approximately \( 16 \) when rounded to the nearest whole number.

Would you like any further clarification or details on this? 

Here are 5 related questions to expand on this topic:
1. How does the Pythagorean theorem apply to other shapes besides right triangles?
2. What would happen if the triangle was not a right triangle?
3. How can the Pythagorean theorem be used in real-world applications?
4. What are other methods to calculate the length of a triangle's side besides the Pythagorean theorem?
5. How do you calculate the distance between two points in 3D space using a similar method?

**Tip:** Always double-check your calculations when dealing with square roots and rounding, especially in applied problems.

Use the information given in the figure to find the length LN.

Learn how to find the length of LN in a right triangle using the Pythagorean theorem. This problem involves multiple applications of the theorem, suitable for students in Grades 8-10.

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