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Question

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

(1 point)
Responses

x=33x is equal to 33

x=9x is equal to 9

x=85.8x is equal to 85 point 8

x=1,089x is equal to 1 comma 089

Answer 1

To determine which value of \( x \) will make the set \( (x, 56, 65) \) a Pythagorean triple, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the two shorter sides equals the square of the longest side.

Given that 65 is the largest number, the equation would look like this:

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

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

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

Now we substitute these values into the equation:

\[ x^2 + 3136 = 4225 \]

To find \( x^2 \), we subtract \( 3136 \) from both sides:

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

Now we take the square root of both sides:

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

Since the question specifies that \( x \) must be less than 65, \( x = 33 \) is the valid answer.

Thus, the correct response is: x=33 (x is equal to 33).