Question
Given that (20,x,29) is a Pythagorean triple and x<29, what is the value of x?
Answers
GPT-4o mini
To determine the value of \( x \) in the Pythagorean triple \( (20, x, 29) \) with the condition \( x < 29 \), we start by using the property of Pythagorean triples. The equation can be expressed as follows, since in a Pythagorean triple \( a^2 + b^2 = c^2 \):
\[
20^2 + x^2 = 29^2
\]
Calculating \( 20^2 \) and \( 29^2 \):
\[
20^2 = 400
\]
\[
29^2 = 841
\]
Now substitute these values into the equation:
\[
400 + x^2 = 841
\]
Next, we isolate \( x^2 \) by subtracting \( 400 \) from both sides:
\[
x^2 = 841 - 400
\]
\[
x^2 = 441
\]
Now we take the square root of both sides to find \( x \):
\[
x = \sqrt{441}
\]
\[
x = 21
\]
Since \( x < 29 \) is satisfied by \( x = 21 \), we conclude that:
\[
\boxed{21}
\] is the value of \( x \).
\[
20^2 + x^2 = 29^2
\]
Calculating \( 20^2 \) and \( 29^2 \):
\[
20^2 = 400
\]
\[
29^2 = 841
\]
Now substitute these values into the equation:
\[
400 + x^2 = 841
\]
Next, we isolate \( x^2 \) by subtracting \( 400 \) from both sides:
\[
x^2 = 841 - 400
\]
\[
x^2 = 441
\]
Now we take the square root of both sides to find \( x \):
\[
x = \sqrt{441}
\]
\[
x = 21
\]
Since \( x < 29 \) is satisfied by \( x = 21 \), we conclude that:
\[
\boxed{21}
\] is the value of \( x \).