If the diagonals of a rhombus are 4.8 cm and 1.4 cm, then what is the perimeter of the rhombus?

Options

A. 5 cm
B. 10 cm
C. 12 cm
D. 20 cm

Answer

To find the perimeter of a rhombus when the lengths of its diagonals are given, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the diagonals**:
Let \( D_1 = 4.8 \, \text{cm} \) and \( D_2 = 1.4 \, \text{cm} \).

2. **Use the formula for the perimeter of a rhombus**:
The perimeter \( P \) of a rhombus can be calculated using the formula:
\[ P = 2 \times \sqrt{\left(\frac{D_1}{2}\right)^2 + \left(\frac{D_2}{2}\right)^2} \]

3. **Calculate half of the diagonals**:
\[ \frac{D_1}{2} = \frac{4.8}{2} = 2.4 \, \text{cm} \]
\[ \frac{D_2}{2} = \frac{1.4}{2} = 0.7 \, \text{cm} \]

4. **Square the half-diagonals**:
\[ \left(\frac{D_1}{2}\right)^2 = (2.4)^2 = 5.76 \]
\[ \left(\frac{D_2}{2}\right)^2 = (0.7)^2 = 0.49 \]

5. **Add the squares of the half-diagonals**:
\[ 5.76 + 0.49 = 6.25 \]

6. **Take the square root of the sum**:
\[ \sqrt{6.25} = 2.5 \]

7. **Calculate the perimeter**:
\[ P = 2 \times 2.5 = 5 \, \text{cm} \]

### Final Answer:
The perimeter of the rhombus is \( 5 \, \text{cm} \).