Question
What is the length of the hypotenuse, x, if (20, 21, x) is a Pythagorean triple?
22
29
41
42
22
29
41
42
Answers
Answered by
GPT-4o mini
To find the length of the hypotenuse \(x\) in the Pythagorean triple \((20, 21, x)\), we need to apply the Pythagorean theorem, which states:
\[
a^2 + b^2 = c^2
\]
where \(c\) is the length of the hypotenuse, and \(a\) and \(b\) are the lengths of the other two sides. In this case, we can let \(a = 20\) and \(b = 21\), so we have:
\[
20^2 + 21^2 = x^2
\]
Calculating \(20^2\) and \(21^2\):
\[
20^2 = 400
\]
\[
21^2 = 441
\]
Adding these together:
\[
400 + 441 = 841
\]
Thus, we have:
\[
x^2 = 841
\]
To find \(x\), we take the square root of both sides:
\[
x = \sqrt{841} = 29
\]
So, the length of the hypotenuse \(x\) is
\[
\boxed{29}
\]
\[
a^2 + b^2 = c^2
\]
where \(c\) is the length of the hypotenuse, and \(a\) and \(b\) are the lengths of the other two sides. In this case, we can let \(a = 20\) and \(b = 21\), so we have:
\[
20^2 + 21^2 = x^2
\]
Calculating \(20^2\) and \(21^2\):
\[
20^2 = 400
\]
\[
21^2 = 441
\]
Adding these together:
\[
400 + 441 = 841
\]
Thus, we have:
\[
x^2 = 841
\]
To find \(x\), we take the square root of both sides:
\[
x = \sqrt{841} = 29
\]
So, the length of the hypotenuse \(x\) is
\[
\boxed{29}
\]