Given that $20$, $21$, and $x$ form a Pythagorean triple, what is the value of $x$?

• A. $22$
• B. $42$
• C. $41$
• D. $29$

Answer: (C)

Verified step by step guidance

1. Recall that a Pythagorean triple consists of three positive integers \(a\), \(b\), and \(c\) such that \(a^2 + b^2 = c^2\), where \(c\) is the hypotenuse (the longest side).
2. Identify the two given sides: 20 and 21. We need to determine if \(x\) is the hypotenuse or one of the legs. Since 21 is larger than 20, if \(x\) is larger than both, it will be the hypotenuse; otherwise, it will be a leg.
3. Assuming \(x\) is the hypotenuse, set up the Pythagorean equation: \(20^2 + 21^2 = x^2\).
4. Calculate the squares of the known sides: \(20^2 = 400\) and \(21^2 = 441\), then add them: \(400 + 441 = 841\).
5. Take the square root of 841 to find \(x\): \(x = \sqrt{841}\). This will give the value of \(x\) that completes the Pythagorean triple.