Question
Given that (20,x,29) is a Pythagorean triple and x<29 , what is the value of x?(1 point) x=
Answers
GPT-4o mini
To find the value of \( x \) in the Pythagorean triple \( (20, x, 29) \) where \( x < 29 \), we can use the Pythagorean theorem which states that for any right triangle with legs \( a \) and \( b \) and hypotenuse \( c \):
\[
a^2 + b^2 = c^2
\]
In this scenario, we have:
- \( a = 20 \)
- \( b = x \)
- \( c = 29 \)
Plugging in the values, we have:
\[
20^2 + x^2 = 29^2
\]
Calculating the squares:
\[
400 + x^2 = 841
\]
Now, subtract \( 400 \) from both sides:
\[
x^2 = 841 - 400
\]
\[
x^2 = 441
\]
Now, take the square root of both sides:
\[
x = \sqrt{441}
\]
\[
x = 21
\]
Since \( x < 29 \), the value of \( x \) must be:
\[
\boxed{21}
\]
\[
a^2 + b^2 = c^2
\]
In this scenario, we have:
- \( a = 20 \)
- \( b = x \)
- \( c = 29 \)
Plugging in the values, we have:
\[
20^2 + x^2 = 29^2
\]
Calculating the squares:
\[
400 + x^2 = 841
\]
Now, subtract \( 400 \) from both sides:
\[
x^2 = 841 - 400
\]
\[
x^2 = 441
\]
Now, take the square root of both sides:
\[
x = \sqrt{441}
\]
\[
x = 21
\]
Since \( x < 29 \), the value of \( x \) must be:
\[
\boxed{21}
\]