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The problem is given in Indonesian and states:

**2. Sebuah segitiga sisi-sisinya 3a cm, 4a cm, dan 5a cm:**

- **(a)** Jika kelilingnya tak lebih dari 120, berapakah nilai \( a \) yang mungkin?
- **(b)** Berapa luas segitiga tersebut?

Let's solve each part:

### Part (a): Finding Possible Values for \( a \)
The triangle has side lengths \( 3a \), \( 4a \), and \( 5a \). The perimeter of the triangle must not exceed 120 cm.

1. The perimeter of the triangle is:
   \[
   3a + 4a + 5a = 12a
   \]

2. According to the condition, the perimeter cannot exceed 120:
   \[
   12a \leq 120
   \]

3. Solve for \( a \):
   \[
   a \leq \frac{120}{12}
   \]
   \[
   a \leq 10
   \]

Thus, the possible values for \( a \) are \( a \leq 10 \).

### Part (b): Calculating the Area of the Triangle
To find the area, we can use **Heron's formula**. First, let's calculate the semi-perimeter \( s \).

1. **Calculate Semi-perimeter \( s \):**
   \[
   s = \frac{3a + 4a + 5a}{2} = \frac{12a}{2} = 6a
   \]

2. **Use Heron's Formula for the Area**:
   The area \( A \) is given by:
   \[
   A = \sqrt{s(s - 3a)(s - 4a)(s - 5a)}
   \]

   Substitute \( s = 6a \):
   \[
   A = \sqrt{6a \cdot (6a - 3a) \cdot (6a - 4a) \cdot (6a - 5a)}
   \]
   \[
   = \sqrt{6a \cdot 3a \cdot 2a \cdot a}
   \]
   \[
   = \sqrt{36a^4}
   \]
   \[
   = 6a^2
   \]

Therefore, the area of the triangle is \( 6a^2 \) square centimeters.

### Final Answer:
- **(a)** \( a \leq 10 \)
- **(b)** Area \( = 6a^2 \) cm²

Would you like further clarification on any steps?

---

**Relative Questions:**
1. How does the perimeter constraint affect the possible values of \( a \)?
2. What would happen to the area if \( a \) were exactly 10?
3. How is Heron's formula used to calculate the area of triangles with given side lengths?
4. What is the significance of semi-perimeter in triangle area calculations?
5. Can we solve this using trigonometry instead of Heron's formula?

**Tip:** Always verify if side lengths satisfy the triangle inequality when given variable sides.

Sebuah segitiga sisi-sisinya 3a cm, 4a cm, dan 5a cm:

a. Jika kelilingnya tak lebih dari 120, berapakah nilai a yang mungkin?
b. Berapa luas segitiga tersebut?

Solve a triangle problem involving sides of lengths 3a cm, 4a cm, and 5a cm. Learn how to find possible values of a when the perimeter is no more than 120 cm, and calculate the area using Heron's formula. Suitable for Grades 8-10.

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