Question

(16, x, 34) is a Pythagorean triple. If 16<x<34 , what is the value of x ?(1 point)
Responses

25
25

28
28

32
32

30

Answer 1

To determine the value of \( x \) in the Pythagorean triple \( (16, x, 34) \), we can use the Pythagorean theorem, which states that for a right triangle with sides \( a \), \( b \), and hypotenuse \( c \):

\[
a^2 + b^2 = c^2
\]

Here, let \( a = 16 \), \( b = x \), and \( c = 34 \). Thus, we can write the equation as:

\[
16^2 + x^2 = 34^2
\]

Now, calculate \( 16^2 \) and \( 34^2 \):

\[
16^2 = 256
\]
\[
34^2 = 1156
\]

Substituting these values into the equation gives:

\[
256 + x^2 = 1156
\]

Next, isolate \( x^2 \) by subtracting \( 256 \) from both sides:

\[
x^2 = 1156 - 256
\]
\[
x^2 = 900
\]

Taking the square root of both sides results in:

\[
x = \sqrt{900} = 30
\]

Since \( 16 < x < 34 \), we confirm \( x = 30 \) is within the specified range.

Therefore, the value of \( x \) is:

\[
\boxed{30}
\]