Question
Given that (10,24,x) is a Pythagorean triple and x > 24, what is the value of x?
Answers
GPT-4o mini
To determine \( x \) in the Pythagorean triple \( (10, 24, x) \) where \( x > 24 \), we start by using the Pythagorean theorem:
\[
a^2 + b^2 = c^2
\]
In this case, let \( a = 10 \), \( b = 24 \), and \( c = x \). Therefore, we have:
\[
10^2 + 24^2 = x^2
\]
Calculating \( 10^2 \) and \( 24^2 \):
\[
10^2 = 100
\]
\[
24^2 = 576
\]
Now, adding these two values:
\[
100 + 576 = 676
\]
Setting this equal to \( x^2 \):
\[
x^2 = 676
\]
Next, we find \( x \) by taking the square root of both sides:
\[
x = \sqrt{676}
\]
Calculating the square root:
\[
x = 26
\]
Since the problem specifies that \( x > 24 \), this condition holds. Therefore, the value of \( x \) is:
\[
\boxed{26}
\]
\[
a^2 + b^2 = c^2
\]
In this case, let \( a = 10 \), \( b = 24 \), and \( c = x \). Therefore, we have:
\[
10^2 + 24^2 = x^2
\]
Calculating \( 10^2 \) and \( 24^2 \):
\[
10^2 = 100
\]
\[
24^2 = 576
\]
Now, adding these two values:
\[
100 + 576 = 676
\]
Setting this equal to \( x^2 \):
\[
x^2 = 676
\]
Next, we find \( x \) by taking the square root of both sides:
\[
x = \sqrt{676}
\]
Calculating the square root:
\[
x = 26
\]
Since the problem specifies that \( x > 24 \), this condition holds. Therefore, the value of \( x \) is:
\[
\boxed{26}
\]