In a right triangle ABC,∠B=90 . If AB=14 cm,BC=48 cm, find AC.

Options

A. 50
B. 48
C. 20
D. 26

Answer

To find the length of side AC in the right triangle ABC where ∠B = 90°, AB = 14 cm, and BC = 48 cm, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (AC) is equal to the sum of the squares of the lengths of the other two sides (AB and BC).

### Step-by-Step Solution:

1. **Identify the sides of the triangle**:
- AB = 14 cm (one leg)
- BC = 48 cm (the other leg)
- AC = ? (the hypotenuse)

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

3. **Substitute the known values into the equation**:
\[ AC^2 = (14)^2 + (48)^2 \]

4. **Calculate the squares of AB and BC**:
\[ AC^2 = 196 + 2304 \]

5. **Add the results**:
\[ AC^2 = 2500 \]

6. **Take the square root of both sides to find AC**:
\[ AC = \sqrt{2500} \]

7. **Calculate the square root**:
\[ AC = 50 \text{ cm} \]

### Final Answer:
The length of AC is 50 cm.

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