The area of a rhombus is `148.8 cm^(2)`. If one of its diagonals is 19.2 cm, find the length of the other diagonal.

Answer

To find the length of the other diagonal of the rhombus, we can use the formula for the area of a rhombus, which is given by:

\[ \text{Area} = \frac{1}{2} \times d_1 \times d_2 \]

where \(d_1\) and \(d_2\) are the lengths of the diagonals.

### Step-by-step Solution:

1. **Identify the given values**:
- Area of the rhombus \(A = 148.8 \, \text{cm}^2\)
- One diagonal \(d_1 = 19.2 \, \text{cm}\)
- The other diagonal \(d_2\) is what we need to find.

2. **Substitute the known values into the area formula**:
\[ 148.8 = \frac{1}{2} \times 19.2 \times d_2 \]

3. **Multiply both sides by 2 to eliminate the fraction**:
\[ 2 \times 148.8 = 19.2 \times d_2 \]
\[ 297.6 = 19.2 \times d_2 \]

4. **Now, divide both sides by 19.2 to solve for \(d_2\)**:
\[ d_2 = \frac{297.6}{19.2} \]

5. **Perform the division**:
- First, simplify the division:
\[ d_2 = \frac{2976}{192} \quad (\text{Multiplying both numerator and denominator by 10}) \]
- Now, divide:
\[ d_2 = 15.5 \, \text{cm} \]

### Final Answer:
The length of the other diagonal \(d_2\) is \(15.5 \, \text{cm}\).

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