The area of a rhombus is 150 `cm^(2)`. The length of one of its diagonal is 10 cm. What is 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 in terms of its diagonals.

### Step-by-Step Solution:

1. **Understand the Area Formula**: The area \( A \) of a rhombus can be calculated using the formula:
\[ A = \frac{1}{2} \times d_1 \times d_2 \]
where \( d_1 \) and \( d_2 \) are the lengths of the diagonals.

2. **Substitute Given Values**: We know the area \( A = 150 \, \text{cm}^2 \) and one diagonal \( d_1 = 10 \, \text{cm} \). We need to find the other diagonal \( d_2 \). Substitute the known values into the formula:
\[ 150 = \frac{1}{2} \times 10 \times d_2 \]

3. **Simplify the Equation**: To eliminate the fraction, multiply both sides by 2:
\[ 300 = 10 \times d_2 \]

4. **Solve for \( d_2 \)**: Now, divide both sides by 10 to isolate \( d_2 \):
\[ d_2 = \frac{300}{10} = 30 \, \text{cm} \]

5. **Conclusion**: The length of the other diagonal \( d_2 \) is 30 cm.

### Final Answer:
The length of the other diagonal is **30 cm**.