What value of x that is less than 65 will make the set (x,56,65)

Question

a Pythagorean triple?(1 point)
Responses

x=33
x equals 33

x=9
x equals 9

x=85.8
x equals 85.8

x=1,089

Answer 1

To determine which value of \( x \) less than 65 can form a Pythagorean triple with the numbers 56 and 65, we can use the Pythagorean theorem. In a Pythagorean triple, the relationship is:

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

where \( c \) is the largest number. In this case, 65 is the largest number, so we have:

\[ x^2 + 56^2 = 65^2 \]

Calculating \( 56^2 \) and \( 65^2 \):

\[ 56^2 = 3136 \] \[ 65^2 = 4225 \]

Substituting these into the equation:

\[ x^2 + 3136 = 4225 \]

Now, we isolate \( x^2 \):

\[ x^2 = 4225 - 3136 \] \[ x^2 = 1089 \]

Now, take the square root of both sides:

\[ x = \sqrt{1089} = 33 \]

This value of \( x \) is less than 65. Therefore, the correct response is:

x equals 33.