The area of a rhombus is 243 `cm^(2)` .If one of the diagonals is 19.5 cm long , find the length of the other diagonal.

Answer

To find the length of the other diagonal of the rhombus, we can follow these steps:

### Step 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.

### Step 2: Identify the given values
From the problem, we know:
- Area \( A = 243 \, \text{cm}^2 \)
- One diagonal \( D_1 = 19.5 \, \text{cm} \)

We need to find the length of the other diagonal \( D_2 \).

### Step 3: Substitute the known values into the area formula
We can substitute the known values into the area formula:
\[ 243 = \frac{1}{2} \times 19.5 \times D_2 \]

### Step 4: Solve for \( D_2 \)
To isolate \( D_2 \), we first multiply both sides of the equation by 2:
\[ 2 \times 243 = 19.5 \times D_2 \]
\[ 486 = 19.5 \times D_2 \]

Next, we divide both sides by 19.5 to solve for \( D_2 \):
\[ D_2 = \frac{486}{19.5} \]

### Step 5: Calculate \( D_2 \)
Now, we perform the division:
\[ D_2 = 24.92 \, \text{cm} \]

### Final Answer
The length of the other diagonal \( D_2 \) is approximately \( 24.92 \, \text{cm} \).

---