The area of a rhombus whose diagonals are 10 cm and 12 cm is `x" cm"^2`. The value of `x` is

Answer

To find the area of a rhombus when the lengths of its diagonals are given, we can use the formula:

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

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

### Step-by-Step Solution:

1. **Identify the lengths of the diagonals**:
- Given \(d_1 = 10 \, \text{cm}\)
- Given \(d_2 = 12 \, \text{cm}\)

2. **Substitute the values into the area formula**:
\[ \text{Area} = \frac{1}{2} \times 10 \, \text{cm} \times 12 \, \text{cm} \]

3. **Calculate the product of the diagonals**:
\[ 10 \times 12 = 120 \, \text{cm}^2 \]

4. **Multiply by \(\frac{1}{2}\)**:
\[ \text{Area} = \frac{120}{2} \, \text{cm}^2 = 60 \, \text{cm}^2 \]

5. **Conclude the value of \(x\)**:
- Since the area of the rhombus is \(60 \, \text{cm}^2\), we have \(x = 60\).

### Final Answer:
The value of \(x\) is \(60\).