Question
Given that (20,x,29) is a Pythagorean triple and x<29, what is the value of x?(1 point)
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x =
Answers
GPT-4o mini
To determine the value of \( x \) in the Pythagorean triple (20, x, 29), we can use the Pythagorean theorem, which states that for a right triangle with legs \( a \) and \( b \), and hypotenuse \( c \):
\[
a^2 + b^2 = c^2
\]
In this case, we can assume \( a = 20 \), \( b = x \), and \( c = 29 \). According to the theorem, we have:
\[
20^2 + x^2 = 29^2
\]
Calculating \( 20^2 \) and \( 29^2 \):
\[
20^2 = 400
\]
\[
29^2 = 841
\]
Now, substituting these values into the equation:
\[
400 + x^2 = 841
\]
Next, we need to solve for \( x^2 \):
\[
x^2 = 841 - 400
\]
\[
x^2 = 441
\]
Taking the square root of both sides:
\[
x = \sqrt{441}
\]
\[
x = 21
\]
Since we have the condition that \( x < 29 \), the value of \( x \) satisfies this condition.
Thus, the value of \( x \) is:
\[
\boxed{21}
\]
\[
a^2 + b^2 = c^2
\]
In this case, we can assume \( a = 20 \), \( b = x \), and \( c = 29 \). According to the theorem, we have:
\[
20^2 + x^2 = 29^2
\]
Calculating \( 20^2 \) and \( 29^2 \):
\[
20^2 = 400
\]
\[
29^2 = 841
\]
Now, substituting these values into the equation:
\[
400 + x^2 = 841
\]
Next, we need to solve for \( x^2 \):
\[
x^2 = 841 - 400
\]
\[
x^2 = 441
\]
Taking the square root of both sides:
\[
x = \sqrt{441}
\]
\[
x = 21
\]
Since we have the condition that \( x < 29 \), the value of \( x \) satisfies this condition.
Thus, the value of \( x \) is:
\[
\boxed{21}
\]