(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

1 answer

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:

\[ \boxed{24} \]