The area of a rhombus is `150 cm^(2)`. The length of one of its diagonals is 10 cm. The length of the other diagonal is : 

Options

A. 25 cm
B. 30 cm
C. 35 cm
D. 40 cm

Answer

To find the length of the other diagonal of a rhombus when the area and one diagonal are given, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Formula for the Area of a Rhombus**:
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. **Identify the Given Values**:
From the question, we know:
- Area \( A = 150 \, \text{cm}^2 \)
- Length of one diagonal \( d_1 = 10 \, \text{cm} \)

3. **Substitute the Known Values into the Formula**:
Plugging the known values into the area formula:
\[ 150 = \frac{1}{2} \times 10 \times d_2 \]

4. **Simplify the Equation**:
First, simplify the right side:
\[ 150 = 5 \times d_2 \]

5. **Solve for the Other Diagonal \( d_2 \)**:
To find \( d_2 \), divide both sides of the equation by 5:
\[ d_2 = \frac{150}{5} = 30 \, \text{cm} \]

6. **Conclusion**:
Therefore, the length of the other diagonal \( d_2 \) is \( 30 \, \text{cm} \).

### Final Answer:
The length of the other diagonal is \( 30 \, \text{cm} \).

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