Which value of x will make (x, 63, 65) a Pythagorean triple?

To determine which value of \( x \) will make \( (x, 63, 65) \) a Pythagorean triple, we need to check if \( x^2 + 63^2 = 65^2 \).

First, calculate \( 63^2 \) and \( 65^2 \):

\[ 63^2 = 3969 \]

\[ 65^2 = 4225 \]

Now, we can set up the equation:

\[ x^2 + 3969 = 4225 \]

Subtract 3969 from both sides:

\[ x^2 = 4225 - 3969 \]

Calculate the right side:

\[ 4225 - 3969 = 256 \]

So, we have:

\[ x^2 = 256 \]

Taking the square root of both sides gives:

\[ x = 16 \]

Thus, the value of \( x \) that makes \( (x, 63, 65) \) a Pythagorean triple is:

\[ \boxed{16} \]