Which equation can be used to find $x$, the length of the hypotenuse of a right triangle with legs of lengths $a$ and $b$?

• A. $x^2=a^2-b^2$
• B. $x=a+b$
• C. $x^2=a^2+b^2$
• D. $x=a^2+b^2$

Answer: (C)

Verified step by step guidance

1. Recall the Pythagorean theorem, which relates the lengths of the sides of a right triangle: the square of the hypotenuse equals the sum of the squares of the legs.
2. Identify the hypotenuse as the side opposite the right angle, labeled as \(x\), and the legs as \(a\) and \(b\).
3. Write the Pythagorean theorem formula: \(x^{2} = a^{2} + b^{2}\).
4. Understand that this equation allows you to find the length of the hypotenuse \(x\) when the lengths of the legs \(a\) and \(b\) are known.
5. Note that the other given equations do not correctly represent the relationship in a right triangle, so they cannot be used to find \(x\).