Three numbers a,b and c form a Phythagorean triplet. If a=5, b=12, find c if c is the largest of the three numbers.

Answer

To solve the problem of finding the value of \( c \) in the Pythagorean triplet where \( a = 5 \) and \( b = 12 \), we will follow these steps:

### Step-by-Step Solution:

1. **Understand the Pythagorean Theorem**:
The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be expressed as:
\[ c^2 = a^2 + b^2 \]

2. **Identify the values**:
Given that \( a = 5 \) and \( b = 12 \), we will substitute these values into the Pythagorean theorem.

3. **Substitute the values into the theorem**:
\[ c^2 = 5^2 + 12^2 \]

4. **Calculate \( 5^2 \) and \( 12^2 \)**:
\[ 5^2 = 25 \]
\[ 12^2 = 144 \]

5. **Add the squares**:
\[ c^2 = 25 + 144 \]
\[ c^2 = 169 \]

6. **Find the value of \( c \)**:
To find \( c \), take the square root of both sides:
\[ c = \sqrt{169} \]
\[ c = 13 \]

### Final Answer:
Thus, the value of \( c \) is \( 13 \).

---