Question
Given that (20,x,29) is a Pythagorean triple and x<29, what is the value of x?(1 point)
x =
x =
Answers
GPT-4o mini
In a Pythagorean triple, the relationship among the three numbers \(a\), \(b\), and \(c\) can be expressed as:
\[
a^2 + b^2 = c^2
\]
Given the triple \((20, x, 29)\), we identify \(a = 20\), \(b = x\), and \(c = 29\).
We can set up the equation:
\[
20^2 + x^2 = 29^2
\]
Calculating \(20^2\) and \(29^2\):
\[
20^2 = 400
\]
\[
29^2 = 841
\]
Substituting these values into the equation gives:
\[
400 + x^2 = 841
\]
To find \(x^2\), we rearrange the equation:
\[
x^2 = 841 - 400
\]
\[
x^2 = 441
\]
Taking the square root of both sides:
\[
x = \sqrt{441}
\]
\[
x = 21
\]
Since \(x < 29\) is satisfied, we conclude:
\[
\boxed{21}
\]
\[
a^2 + b^2 = c^2
\]
Given the triple \((20, x, 29)\), we identify \(a = 20\), \(b = x\), and \(c = 29\).
We can set up the equation:
\[
20^2 + x^2 = 29^2
\]
Calculating \(20^2\) and \(29^2\):
\[
20^2 = 400
\]
\[
29^2 = 841
\]
Substituting these values into the equation gives:
\[
400 + x^2 = 841
\]
To find \(x^2\), we rearrange the equation:
\[
x^2 = 841 - 400
\]
\[
x^2 = 441
\]
Taking the square root of both sides:
\[
x = \sqrt{441}
\]
\[
x = 21
\]
Since \(x < 29\) is satisfied, we conclude:
\[
\boxed{21}
\]