Question

which expression represents the length of the hypotenuse, c, of the triangle below?

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle with legs of lengths \(a\) and \(b\) and hypotenuse of length \(c\), the formula is \(a^{2}+b^{2}=c^{2}\).

Step2: Solve for \(c\)

Taking the square root of both sides of the equation \(a^{2}+b^{2}=c^{2}\), we get \(c = \sqrt{a^{2}+b^{2}}\) (since \(c>0\) as it represents the length of a side of a triangle).

Answer:

\(\sqrt{a^{2}+b^{2}}\)