Question

Given that (10,24,x) is a Pythagorean triple and x>24 , what is the value of x?(1 point)

Answer 1

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

\[
\boxed{26}
\]