Is the triangle with sides 25 cm, 5 cm and 24 cm a right triangle? Give reason for your answer.

Options

A. No, not satisfy pythagoras theorem
B. Yes
C. not sure
D. No, not satisfied Thales Theorem

Explanation

To determine if the triangle with sides 25 cm, 5 cm, and 24 cm is a right triangle, 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**:
- Given sides are 25 cm, 5 cm, and 24 cm.
- The longest side is 25 cm, which we will consider as the hypotenuse (let's call it side A).
- The other two sides are 5 cm (side B) and 24 cm (side C).

2. **Apply the Pythagorean theorem**:
- According to the theorem, for a right triangle, the following equation must hold true:
\[ A^2 = B^2 + C^2 \]
- Here, substituting the values:
\[ 25^2 = 5^2 + 24^2 \]

3. **Calculate the squares of the sides**:
- Calculate \(25^2\):
\[ 25^2 = 625 \]
- Calculate \(5^2\):
\[ 5^2 = 25 \]
- Calculate \(24^2\):
\[ 24^2 = 576 \]

4. **Add the squares of the two shorter sides**:
- Now, add \(5^2\) and \(24^2\):
\[ 5^2 + 24^2 = 25 + 576 = 601 \]

5. **Compare the results**:
- Now we compare \(A^2\) and \(B^2 + C^2\):
\[ 625 \neq 601 \]
- Since \(625\) is not equal to \(601\), the condition of the Pythagorean theorem is not satisfied.

6. **Conclusion**:
- Therefore, the triangle with sides 25 cm, 5 cm, and 24 cm is **not a right triangle**.