Question

in the right triangle shown, the length of $overline{ac}=5$ and the length of $overline{bc}=4$. what is the length of $overline{ab}$? choose 1 answer: a $sqrt{3}$ b 3 c $sqrt{41}$ d 41

Explanation:

Step1: Recall Pythagorean theorem

In a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse and \(a\) and \(b\) are the legs. Here, if \(AC = a = 5\) and \(BC=b = 4\), and \(AB\) is the hypotenuse.

Step2: Apply the formula

\(AB=\sqrt{AC^{2}+BC^{2}}=\sqrt{5^{2}+4^{2}}=\sqrt{25 + 16}=\sqrt{41}\)

Answer:

C. \(\sqrt{41}\)