To determine the value of \( x \) that will make \( (x, 63, 65) \) a Pythagorean triple, we can use the Pythagorean theorem, which 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 other two sides.
In this case, we have:
\[ 65^2 = x^2 + 63^2 \]
Calculating \( 65^2 \) and \( 63^2 \):
\[ 65^2 = 4225 \] \[ 63^2 = 3969 \]
Now we substitute these values into the equation:
\[ 4225 = x^2 + 3969 \]
Next, we isolate \( x^2 \):
\[ x^2 = 4225 - 3969 \] \[ x^2 = 256 \]
Taking the square root of both sides gives:
\[ x = 16 \]
Therefore, the value of \( x \) that will make \( (x, 63, 65) \) a Pythagorean triple is:
\[ \boxed{16} \]
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