If diagonals of a rhombus are 12 cm and 16 cm, then what is the perimeter (in cm) of the rhombus?

Options

A. 20
B. 40
C. 60
D. 80

Answer

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

### Step-by-Step Solution:

1. **Identify the lengths of the diagonals**:
The diagonals of the rhombus are given as 12 cm and 16 cm.

2. **Calculate the lengths of the half diagonals**:
Since the diagonals bisect each other at right angles, we can find the lengths of the segments formed by the diagonals:
- Half of the first diagonal (12 cm) = 12 cm / 2 = 6 cm
- Half of the second diagonal (16 cm) = 16 cm / 2 = 8 cm

3. **Use the Pythagorean theorem to find the length of a side of the rhombus**:
Each side of the rhombus can be found using the right triangle formed by the half diagonals. Let’s denote the length of a side as \( s \):
\[ s^2 = (6 \text{ cm})^2 + (8 \text{ cm})^2 \]
\[ s^2 = 36 + 64 = 100 \]
\[ s = \sqrt{100} = 10 \text{ cm} \]

4. **Calculate the perimeter of the rhombus**:
The perimeter \( P \) of a rhombus is given by:
\[ P = 4 \times s \]
Substituting the value of \( s \):
\[ P = 4 \times 10 \text{ cm} = 40 \text{ cm} \]

### Final Answer:
The perimeter of the rhombus is **40 cm**.

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