Question
Which value of x will male (x,63,65) a Pythagorean triple?
A. x=2
B. x=16
C. x = 256
D. x=√8,194
A. x=2
B. x=16
C. x = 256
D. x=√8,194
Answers
GPT-4o mini
To determine which value of \( x \) will make \( (x, 63, 65) \) a Pythagorean triple, we can use the Pythagorean theorem, which states that for a right triangle with sides \( a \), \( b \), and hypotenuse \( c \):
\[
a^2 + b^2 = c^2
\]
In this case, we can assume that \( 65 \) is the hypotenuse since it's the largest number. Therefore, we need to check the equation:
\[
x^2 + 63^2 = 65^2
\]
Calculating \( 63^2 \) and \( 65^2 \):
\[
63^2 = 3969
\]
\[
65^2 = 4225
\]
Now we can substitute these values into the equation:
\[
x^2 + 3969 = 4225
\]
Subtracting \( 3969 \) from both sides gives:
\[
x^2 = 4225 - 3969 = 256
\]
Now, taking the square root of both sides results in:
\[
x = \sqrt{256} = 16
\]
Thus, the value of \( x \) that makes \( (x, 63, 65) \) a Pythagorean triple is \( \boxed{16} \).
\[
a^2 + b^2 = c^2
\]
In this case, we can assume that \( 65 \) is the hypotenuse since it's the largest number. Therefore, we need to check the equation:
\[
x^2 + 63^2 = 65^2
\]
Calculating \( 63^2 \) and \( 65^2 \):
\[
63^2 = 3969
\]
\[
65^2 = 4225
\]
Now we can substitute these values into the equation:
\[
x^2 + 3969 = 4225
\]
Subtracting \( 3969 \) from both sides gives:
\[
x^2 = 4225 - 3969 = 256
\]
Now, taking the square root of both sides results in:
\[
x = \sqrt{256} = 16
\]
Thus, the value of \( x \) that makes \( (x, 63, 65) \) a Pythagorean triple is \( \boxed{16} \).