Question

in the right triangle shown, the length of $overline{bc}=5$ and the length of $overline{ab}=9$. what is the length of $overline{ac}$? choose 1 answer: a $sqrt{106}$ b 106 c $2sqrt{14}$ d 56

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, \(AB^{2}=AC^{2}+BC^{2}\), so \(AC^{2}=AB^{2}-BC^{2}\).

Step2: Substitute given values

Given \(AB = 9\) and \(BC = 5\), then \(AC^{2}=9^{2}-5^{2}=81 - 25=56\).

Step3: Solve for \(AC\)

\(AC=\sqrt{56}=\sqrt{4\times14}=2\sqrt{14}\)

Answer:

C. \(2\sqrt{14}\)