In `DeltaABC`,AB = 24cm,BC = 10 cm and AC= 26 cm. ls this triangle right triangle?

Answer

To determine if triangle ABC is a right triangle with sides AB = 24 cm, BC = 10 cm, and AC = 26 cm, we can use the Pythagorean theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

### Step-by-step Solution:

1. **Identify the sides of the triangle:**
- AB = 24 cm
- BC = 10 cm
- AC = 26 cm

2. **Determine the longest side:**
- The longest side is AC = 26 cm.

3. **Apply the Pythagorean theorem:**
- According to the theorem, for triangle ABC to be a right triangle, it must hold that:
\[ AC^2 = AB^2 + BC^2 \]
- Substitute the lengths:
\[ 26^2 = 24^2 + 10^2 \]

4. **Calculate the squares:**
- Calculate \(26^2\):
\[ 26^2 = 676 \]
- Calculate \(24^2\):
\[ 24^2 = 576 \]
- Calculate \(10^2\):
\[ 10^2 = 100 \]

5. **Add the squares of the other two sides:**
- Now, add \(24^2\) and \(10^2\):
\[ 576 + 100 = 676 \]

6. **Compare the results:**
- We find that:
\[ 26^2 = 676 \quad \text{and} \quad 24^2 + 10^2 = 676 \]
- Since both sides are equal, we conclude that:
\[ AC^2 = AB^2 + BC^2 \]

7. **Conclusion:**
- Therefore, triangle ABC is a right triangle.