The area of a rhombus is 36 cm and the length of one of its diagonals is 6 cm. The length of the second diagonal is

Options

A. 6cm
B. `6sqrt2cm`
C. 12cm
D. none of these

Answer

To find the length of the second diagonal of the rhombus, we can use the formula for the area of a rhombus in terms of its diagonals. 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.

Given:
- Area \( A = 36 \, \text{cm}^2 \)
- Length of one diagonal \( d_1 = 6 \, \text{cm} \)
- Length of the second diagonal \( d_2 = ? \)

### Step-by-step Solution:

1. **Write down the area formula**:
\[ A = \frac{1}{2} \times d_1 \times d_2 \]

2. **Substitute the known values into the formula**:
\[ 36 = \frac{1}{2} \times 6 \times d_2 \]

3. **Multiply both sides by 2 to eliminate the fraction**:
\[ 2 \times 36 = 6 \times d_2 \]
\[ 72 = 6 \times d_2 \]

4. **Divide both sides by 6 to solve for \( d_2 \)**:
\[ d_2 = \frac{72}{6} \]
\[ d_2 = 12 \, \text{cm} \]

### Final Answer:
The length of the second diagonal \( d_2 \) is \( 12 \, \text{cm} \).

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