Question

(18, x, 30) is a Pythagorean triple. If 18<x<30 , what is the value of x ?(1 point)
Responses

18
18

24
24

28
28

26

Answer 1

To determine the value of \( x \) in the Pythagorean triple \( (18, x, 30) \) with the condition \( 18 < x < 30 \), we need to use the Pythagorean theorem:

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

where \( c \) is the longest side. In this case, \( 30 \) is \( c \), and \( 18 \) is one of the other sides \( a \), so we can write:

\[
18^2 + x^2 = 30^2
\]

Calculating \( 18^2 \) and \( 30^2 \):

\[
18^2 = 324
\]
\[
30^2 = 900
\]

So replacing them in the equation, we have:

\[
324 + x^2 = 900
\]

To find \( x^2 \), we subtract \( 324 \) from both sides:

\[
x^2 = 900 - 324
\]
\[
x^2 = 576
\]

Now, we take the square root of both sides to find \( x \):

\[
x = \sqrt{576}
\]
\[
x = 24
\]

Since \( 18 < 24 < 30 \) satisfies the condition given in the problem, the value of \( x \) is:

\[
\boxed{24}
\]