To determine the value of \(x\) in the Pythagorean triple \((10, 24, x)\) where \(x > 24\), we can use the Pythagorean theorem:
\[ a^2 + b^2 = c^2 \]
Here, \(a = 10\), \(b = 24\), and \(c = x\). So we need to calculate:
\[ 10^2 + 24^2 = x^2 \]
Calculating the squares:
\[ 10^2 = 100 \] \[ 24^2 = 576 \]
Adding them together:
\[ 100 + 576 = 676 \]
Now, we have:
\[ x^2 = 676 \]
To find \(x\), we take the square root of both sides:
\[ x = \sqrt{676} = 26 \]
Since \(x > 24\) is satisfied, the value of \(x\) is
\[ \boxed{26} \]