If in a triangle ABC, BE and CF are two medians perpendicular to each other and if `AB=19` cm and `AC=22 cm` then the length of BC is

Answer

To find the length of side BC in triangle ABC, where BE and CF are medians that are perpendicular to each other, and given that AB = 19 cm and AC = 22 cm, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values**:
- AB = 19 cm
- AC = 22 cm

2. **Use the Property of Medians**:
- When two medians of a triangle are perpendicular to each other, the following relationship holds:
\[ AB^2 + AC^2 = 5 \times BC^2 \]

3. **Substitute the Known Values**:
- Substitute the values of AB and AC into the equation:
\[ 19^2 + 22^2 = 5 \times BC^2 \]

4. **Calculate the Squares**:
- Calculate \(19^2\) and \(22^2\):
\[ 19^2 = 361 \]
\[ 22^2 = 484 \]

5. **Add the Squares**:
- Add the results:
\[ 361 + 484 = 845 \]

6. **Set Up the Equation**:
- Now we have:
\[ 845 = 5 \times BC^2 \]

7. **Solve for \(BC^2\)**:
- Divide both sides by 5:
\[ BC^2 = \frac{845}{5} = 169 \]

8. **Find the Length of BC**:
- Take the square root of both sides to find BC:
\[ BC = \sqrt{169} = 13 \text{ cm} \]

### Final Answer:
The length of side BC is **13 cm**.