Determine which of them are right triangles.
5 cm , 2 cm and 5 cm

Answer

To determine whether the sides 5 cm, 2 cm, and 5 cm can form a right triangle, we will use the Pythagorean theorem. The Pythagorean 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**: We have three sides: 5 cm, 5 cm, and 2 cm. The longest side is 5 cm.

2. **Assign sides**: Let's denote the sides as follows:
- Side a = 5 cm
- Side b = 5 cm
- Side c = 2 cm

3. **Check if it can be a right triangle**: According to the Pythagorean theorem, for these sides to form a right triangle, the following equation must hold true:
\[ c^2 = a^2 + b^2 \]
where c is the hypotenuse (the longest side).

4. **Calculate the squares**:
- \( a^2 = 5^2 = 25 \)
- \( b^2 = 5^2 = 25 \)
- \( c^2 = 2^2 = 4 \)

5. **Check the Pythagorean theorem**:
\[ c^2 = a^2 + b^2 \implies 4 = 25 + 25 \]
\[ 4 \neq 50 \]

6. **Conclusion**: Since \( 4 \) is not equal to \( 50 \), the sides 5 cm, 5 cm, and 2 cm do not satisfy the Pythagorean theorem. Therefore, they do not form a right triangle.