The area of right triangular region is `129.5 cm^(2)`. If one of the sides containing the right angle is 14.8 cm, find the other one.

Answer

To find the length of the other side of the right triangle given the area and one side, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the formula for the area of a triangle**:
The area \( A \) of a right triangle can be calculated using the formula:
\[ A = \frac{1}{2} \times \text{base} \times \text{height} \]
In this case, one of the sides containing the right angle is considered as the base, and we need to find the height.

2. **Identify the given values**:
- Area \( A = 129.5 \, \text{cm}^2 \)
- One side (base) \( b = 14.8 \, \text{cm} \)

3. **Substitute the known values into the area formula**:
\[ 129.5 = \frac{1}{2} \times 14.8 \times h \]
where \( h \) is the height (the other side we want to find).

4. **Multiply both sides by 2 to eliminate the fraction**:
\[ 2 \times 129.5 = 14.8 \times h \]
\[ 259 = 14.8 \times h \]

5. **Solve for \( h \)**:
\[ h = \frac{259}{14.8} \]

6. **Perform the division**:
- First, simplify \( \frac{259}{14.8} \):
\[ h = 17.5 \, \text{cm} \]

7. **Conclusion**:
The length of the other side is \( 17.5 \, \text{cm} \).

### Final Answer:
Hence, the length of the other side is \( 17.5 \, \text{cm} \).