`DeltaABC` is right angled at A. if AB = 24 mm and AC = 7 mm, then BC is

Options

A. 20 mm
B. 25 mm
C. 30 mm
D. 35 mm

Answer

To find the length of side BC in the right-angled triangle ABC, where the right angle is at A, we can use the Pythagorean theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse (BC) is equal to the sum of the squares of the lengths of the other two sides (AB and AC).

### Step-by-Step Solution:

1. **Identify the sides of the triangle**:
- AB = 24 mm (one leg)
- AC = 7 mm (the other leg)
- BC = ? (the hypotenuse)

2. **Apply the Pythagorean theorem**:
According to the theorem:
\[ BC^2 = AB^2 + AC^2 \]

3. **Substitute the known values**:
\[ BC^2 = (24 \, \text{mm})^2 + (7 \, \text{mm})^2 \]

4. **Calculate the squares**:
- \( (24 \, \text{mm})^2 = 576 \, \text{mm}^2 \)
- \( (7 \, \text{mm})^2 = 49 \, \text{mm}^2 \)

5. **Add the squares**:
\[ BC^2 = 576 \, \text{mm}^2 + 49 \, \text{mm}^2 = 625 \, \text{mm}^2 \]

6. **Take the square root to find BC**:
\[ BC = \sqrt{625 \, \text{mm}^2} = 25 \, \text{mm} \]

### Final Answer:
Thus, the length of side BC is **25 mm**.