The area of a rhombus is `441 cm^(2)` and its height is 17.5 cm. Find the length of each side of the rhombus. 

Answer

To find the length of each side of the rhombus given its area and height, we can follow these steps:

### Step 1: Write down the formula for the area of a rhombus.
The area \( A \) of a rhombus can be calculated using the formula:
\[ A = \text{Base} \times \text{Height} \]

### Step 2: Substitute the known values into the formula.
We know the area \( A = 441 \, \text{cm}^2 \) and the height \( h = 17.5 \, \text{cm} \). We can rearrange the formula to find the base:
\[ \text{Base} = \frac{A}{h} \]
Substituting the known values:
\[ \text{Base} = \frac{441 \, \text{cm}^2}{17.5 \, \text{cm}} \]

### Step 3: Calculate the base.
Now, we perform the division:
\[ \text{Base} = \frac{441}{17.5} = 25.2 \, \text{cm} \]

### Step 4: Use the base to find the length of each side of the rhombus.
In a rhombus, all sides are equal. The length of each side can be calculated using the Pythagorean theorem, considering half the base and the height as the two legs of a right triangle formed by the height and half the base:
\[ \text{Side} = \sqrt{\left(\frac{\text{Base}}{2}\right)^2 + h^2} \]
Substituting the values:
\[ \text{Side} = \sqrt{\left(\frac{25.2}{2}\right)^2 + (17.5)^2} \]
Calculating:
\[ \text{Side} = \sqrt{(12.6)^2 + (17.5)^2} \]
\[ = \sqrt{158.76 + 306.25} \]
\[ = \sqrt{465.01} \]
\[ \approx 21.56 \, \text{cm} \]

### Final Answer:
The length of each side of the rhombus is approximately \( 21.56 \, \text{cm} \).

---