If the length of the sides BC and AC of a right angled `DeltaABC` are 3 cm and 4 cm respectively, then the length of hypotenuse will be

Options

A. 5 cm
B. 6 cm
C. 14 cm
D. 100cm

Answer

To find the length of the hypotenuse \( AB \) of the right-angled triangle \( \Delta ABC \) where \( AC = 4 \, \text{cm} \) and \( BC = 3 \, \text{cm} \), we can use the Pythagorean theorem.

### Step-by-Step Solution:

1. **Identify the sides**: In the right-angled triangle \( \Delta ABC \):
- \( AC \) (one leg) = 4 cm
- \( BC \) (the other leg) = 3 cm
- \( AB \) (the hypotenuse) = ?

2. **Apply the Pythagorean theorem**: The theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. This can be expressed as:
\[ AB^2 = AC^2 + BC^2 \]

3. **Substitute the known values**:
\[ AB^2 = (4 \, \text{cm})^2 + (3 \, \text{cm})^2 \]
\[ AB^2 = 16 \, \text{cm}^2 + 9 \, \text{cm}^2 \]

4. **Calculate the sum**:
\[ AB^2 = 25 \, \text{cm}^2 \]

5. **Find the length of the hypotenuse**: To find \( AB \), take the square root of both sides:
\[ AB = \sqrt{25 \, \text{cm}^2} = 5 \, \text{cm} \]

Thus, the length of the hypotenuse \( AB \) is **5 cm**.