In a rhombus of side 10 cm one of the diagonals is 12 cm long. Find the length of second diagonal.

Answer

To find the length of the second diagonal in a rhombus where one diagonal is given, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Information:**
- Side of the rhombus (AB) = 10 cm
- Length of one diagonal (AC) = 12 cm

2. **Understand the Properties of a Rhombus:**
- The diagonals of a rhombus bisect each other at right angles. This means that if we denote the intersection point of the diagonals as O, then AO = OC and BO = OD.

3. **Calculate the Length of AO:**
- Since diagonal AC is 12 cm, we can find AO:
\[ AO = \frac{AC}{2} = \frac{12}{2} = 6 \text{ cm} \]

4. **Use the Pythagorean Theorem in Triangle AOB:**
- In triangle AOB, we can apply the Pythagorean theorem:
\[ AB^2 = AO^2 + BO^2 \]
- Substituting the known values:
\[ 10^2 = 6^2 + BO^2 \]
\[ 100 = 36 + BO^2 \]

5. **Solve for BO:**
- Rearranging the equation gives:
\[ BO^2 = 100 - 36 = 64 \]
- Taking the square root:
\[ BO = \sqrt{64} = 8 \text{ cm} \]

6. **Calculate the Length of the Second Diagonal (BD):**
- Since BD = 2 * BO:
\[ BD = 2 \times 8 = 16 \text{ cm} \]

7. **Final Answer:**
- The length of the second diagonal BD is 16 cm.