The area of a rhombus is `20 cm^(2)`. If one of its diagonals is 5 cm, the other diagonal is

Options

A. 5 cm
B. 6 cm
C. 8 cm
D. 10 cm

Answer

To find the length of the other diagonal of a rhombus when one diagonal and the area are given, we can use the formula for the area of a rhombus in terms of its diagonals.

### 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 problem, we know:
- Area \( A = 20 \, \text{cm}^2 \)
- One diagonal \( d_1 = 5 \, \text{cm} \)

3. **Substitute the known values into the area formula**:
We can rearrange the area formula to solve for the unknown diagonal \( d_2 \):
\[ 20 = \frac{1}{2} \times 5 \times d_2 \]

4. **Multiply both sides by 2 to eliminate the fraction**:
\[ 40 = 5 \times d_2 \]

5. **Divide both sides by 5 to solve for \( d_2 \)**:
\[ d_2 = \frac{40}{5} = 8 \, \text{cm} \]

6. **Conclusion**:
The length of the other diagonal \( d_2 \) is \( 8 \, \text{cm} \).

### Final Answer:
The other diagonal is \( 8 \, \text{cm} \).

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