What is the value of x if 13, 84, x is a Pythagorean triple?(1 point)Responses8686858597979494

To find the value of \( x \) such that \( 13, 84, x \) is a Pythagorean triple, we can use the Pythagorean theorem, which states that for a Pythagorean triple \( a^2 + b^2 = c^2 \), where \( c \) is the hypotenuse.

Assuming \( x \) is the hypotenuse, we have:

\[
13^2 + 84^2 = x^2
\]

Calculating \( 13^2 \) and \( 84^2 \):

\[
13^2 = 169
\]
\[
84^2 = 7056
\]

Now, we add these two values:

\[
169 + 7056 = 7225
\]

Now we find \( x \) by taking the square root of \( 7225 \):

\[
x = \sqrt{7225} = 85
\]

Thus, if \( x \) is the hypotenuse, then \( x = 85 \).

Now we'll also check if \( x \) could be one of the legs (either \( 13 \) or \( 84 \)).

1. If \( 13 \) is the leg and \( x \) is the hypotenuse:
\[
13^2 + x^2 = 84^2
\]
\[
169 + x^2 = 7056
\]
\[
x^2 = 7056 - 169 = 6887
\]
\[
x = \sqrt{6887} \quad (\text{not an integer, disregard it})
\]

2. If \( 84 \) is the leg and \( x \) is the hypotenuse:
\[
13^2 + 84^2 = x^2
\]
We already calculated this above and found \( x = 85 \).

Thus, the value of \( x \) such that \( 13, 84, x \) forms a Pythagorean triple is:

\[
\boxed{85}
\]