If the diagonals of a rhombus are 12cm and 16cm, find the length of each side.

Options

A. 9 cm
B. 10 cm
C. 8 cm
D. 20 cm

Explanation

To find the length of each side of the rhombus given the lengths of its diagonals, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the lengths of the diagonals**:
- Given diagonals: AC = 16 cm and BD = 12 cm.

2. **Understand the properties of the rhombus**:
- The diagonals of a rhombus bisect each other at right angles (90 degrees).

3. **Calculate the lengths of the halves of the diagonals**:
- Since diagonals bisect each other, we can find the lengths of AO and BO.
- AO = AC / 2 = 16 cm / 2 = 8 cm.
- BO = BD / 2 = 12 cm / 2 = 6 cm.

4. **Draw a right triangle**:
- In triangle AOB, we have:
- AO = 8 cm (one leg),
- BO = 6 cm (the other leg),
- AB = the hypotenuse (which is the side of the rhombus).

5. **Apply the Pythagorean theorem**:
- According to the Pythagorean theorem:
\[ AB^2 = AO^2 + BO^2 \]
- Substituting the values:
\[ AB^2 = 8^2 + 6^2 \]
\[ AB^2 = 64 + 36 \]
\[ AB^2 = 100 \]

6. **Calculate the length of the side**:
- Taking the square root of both sides:
\[ AB = \sqrt{100} = 10 \text{ cm} \]

### Conclusion:
The length of each side of the rhombus is **10 cm**.