Question

in the right triangle shown, the length of $overline{ac}=5$ and the length of $overline{bc}=6$. what is the length of $overline{ab}$? choose 1 answer: (a) $sqrt{11}$ (b) $11$ (c) $sqrt{61}$ (d) $61$

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, \(AB^{2}=AC^{2}+BC^{2}\) (where \(AB\) is the hypotenuse). Given \(AC = 5\) and \(BC=6\), we substitute these values into the formula: \(AB^{2}=5^{2}+6^{2}\).

Step2: Calculate the squares

\(5^{2}=25\) and \(6^{2}=36\), so \(AB^{2}=25 + 36\).

Step3: Find the sum

\(25+36=61\), then \(AB=\sqrt{61}\) (since \(AB>0\) as it represents the length of a side).

Answer:

C. \(\sqrt{61}\)