Question

Which value of x will make (36, x, 85) a Pythagorean triple?

(1 point)
Responses

2,159−−−−−√square root of 2 comma 159 end root

77
77

5929
5929

7
7

Answer 1

To determine which value of \( x \) will make \( (36, x, 85) \) a Pythagorean triple, we need to verify if the equation \( 36^2 + x^2 = 85^2 \) holds true.

First, calculate \( 36^2 \) and \( 85^2 \):

\[
36^2 = 1296,
\]
\[
85^2 = 7225.
\]

Now substitute these values into the equation:

\[
1296 + x^2 = 7225.
\]

To solve for \( x^2 \), rearrange the equation:

\[
x^2 = 7225 - 1296.
\]

Now, calculate the right side:

\[
x^2 = 7225 - 1296 = 5929.
\]

Now, take the square root of both sides:

\[
x = \sqrt{5929} = 77.
\]

Therefore, the value of \( x \) that makes \( (36, x, 85) \) a Pythagorean triple is \( \boxed{77} \).