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To solve this problem, we need to use the properties of an isosceles triangle and basic geometry.

### Step-by-step explanation:

1. **Identify the triangle's structure:**
   - \( \triangle LMN \) is an **isosceles triangle**, meaning two of its sides are equal.
   - \( \angle L = \angle N = 63^\circ \), indicating that the triangle is isosceles with the base \( LN \), and the two equal sides are \( LM \) and \( MN \).

2. **Sum of angles in a triangle:**
   - The sum of interior angles in any triangle is always \( 180^\circ \).
   - Let \( \angle M \) be the third angle. Since \( \angle L = 63^\circ \) and \( \angle N = 63^\circ \):
     \[
     \angle M = 180^\circ - 63^\circ - 63^\circ = 54^\circ.
     \]

3. **Side lengths:**
   - The length of side \( LM = 3x \) and the length of side \( MN = x + 8 \).
   - Since \( \triangle LMN \) is isosceles, the two sides \( LM \) and \( MN \) must be equal.
     \[
     3x = x + 8.
     \]

4. **Solve for \( x \):**
   \[
   3x - x = 8,
   \]
   \[
   2x = 8,
   \]
   \[
   x = 4.
   \]

5. **Find the length of \( MN \):**
   - Since \( MN = x + 8 \), substitute \( x = 4 \):
     \[
     MN = 4 + 8 = 12.
     \]

Thus, the length of \( MN \) is **12 units**.

### Answer:
The correct option is **B. 12**.

Would you like a deeper explanation of any step? Here are some related questions you might find interesting:

1. What is the importance of knowing the properties of isosceles triangles in geometry?
2. Can you explain how to solve triangles that are not isosceles or equilateral?
3. How can you apply angle properties in different types of triangles?
4. How would this problem change if the angles were different?
5. What are some real-world applications of isosceles triangles?

**Tip:** Always verify if triangles are isosceles or equilateral before solving for sides and angles, as their properties simplify the solution.

What is the length of side MN in an isosceles triangle where two angles are 63 degrees and the two sides opposite these angles are 3x and x+8?

Learn how to find the length of a side in an isosceles triangle where two angles are 63 degrees and the sides are represented by algebraic expressions. This problem is suitable for students in Grades 7-9 and covers key concepts such as the isosceles triangle properties, sum of angles in a triangle, and basic algebra.

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