In a rhombus, the lengths of diagonals are 16cm and 12cm, The side of the rhombus is

Options

A. 9cm
B. 7cm
C. 8cm
D. 10cm

Answer

To find the side of the rhombus given the lengths of its diagonals, we can use the relationship between the diagonals and the sides of a rhombus.

### Step-by-Step Solution:

1. **Identify the lengths of the diagonals**:
- Let diagonal 1 (d1) = 16 cm
- Let diagonal 2 (d2) = 12 cm

2. **Use the relationship between the diagonals and the side of the rhombus**:
- The formula relating the diagonals and the sides of a rhombus is given by:
\[ d1^2 + d2^2 = 4a^2 \]
where \( a \) is the length of a side of the rhombus.

3. **Substitute the values of the diagonals into the formula**:
\[ 16^2 + 12^2 = 4a^2 \]

4. **Calculate the squares of the diagonals**:
- \( 16^2 = 256 \)
- \( 12^2 = 144 \)

5. **Add the squares of the diagonals**:
\[ 256 + 144 = 400 \]

6. **Set up the equation**:
\[ 400 = 4a^2 \]

7. **Divide both sides by 4**:
\[ a^2 = \frac{400}{4} = 100 \]

8. **Take the square root of both sides to find \( a \)**:
\[ a = \sqrt{100} = 10 \]

9. **State the final answer**:
- The length of the side of the rhombus is \( 10 \) cm.

### Final Answer:
The side of the rhombus is **10 cm**.

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