Sides of triangles are given below . Determine which of them are right triangles . In case of a right triangle write the length of its hypotenuse .
50 cm ,80 cm and 100 cm

Answer

To determine if the triangle with sides 50 cm, 80 cm, and 100 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:**
- Let the sides be \( a = 50 \) cm, \( b = 80 \) cm, and \( c = 100 \) cm.
- Here, \( c \) is the longest side and we will assume it to be the hypotenuse.

2. **Apply the Pythagorean theorem:**
- According to the theorem, for a right triangle, the following must hold:
\[ c^2 = a^2 + b^2 \]
- Substitute the values of \( a \), \( b \), and \( c \):
\[ 100^2 = 50^2 + 80^2 \]

3. **Calculate the squares of the sides:**
- Calculate \( c^2 \):
\[ 100^2 = 10000 \]
- Calculate \( a^2 \):
\[ 50^2 = 2500 \]
- Calculate \( b^2 \):
\[ 80^2 = 6400 \]

4. **Sum \( a^2 \) and \( b^2 \):**
- Now, add \( a^2 \) and \( b^2 \):
\[ 2500 + 6400 = 8900 \]

5. **Compare \( c^2 \) with \( a^2 + b^2 \):**
- We have:
\[ c^2 = 10000 \quad \text{and} \quad a^2 + b^2 = 8900 \]
- Since \( 10000 \neq 8900 \), the Pythagorean theorem does not hold.

6. **Conclusion:**
- Therefore, the triangle with sides 50 cm, 80 cm, and 100 cm is **not a right triangle**.

### Final Answer:
The triangle is not a right triangle.