The area of a rhombus is 216 sq. cm. If its one diagonal is 24 cm, find :
length of its other diagonal,

Answer

To find the length of the other diagonal of a rhombus when given the area and one diagonal, 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. **Substitute the known values into the formula**:
We know the area \( A = 216 \, \text{sq. cm} \) and one diagonal \( d_1 = 24 \, \text{cm} \). We need to find the other diagonal \( d_2 \).
\[ 216 = \frac{1}{2} \times 24 \times d_2 \]

3. **Multiply both sides by 2 to eliminate the fraction**:
\[ 2 \times 216 = 24 \times d_2 \]
\[ 432 = 24 \times d_2 \]

4. **Divide both sides by 24 to solve for \( d_2 \)**:
\[ d_2 = \frac{432}{24} \]

5. **Calculate the value**:
\[ d_2 = 18 \, \text{cm} \]

### Final Answer:
The length of the other diagonal \( d_2 \) is \( 18 \, \text{cm} \).

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