Question

find the length of the hypotenuse in the provided triangle. note that the diagram may not be to scale. 3 √41 6 √31

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle with legs \(a\) and \(b\) and hypotenuse \(c\), \(c^{2}=a^{2}+b^{2}\). Here \(a = 4\) and \(b = 5\).

Step2: Calculate \(a^{2}+b^{2}\)

\(a^{2}=4^{2}=16\), \(b^{2}=5^{2}=25\), then \(a^{2}+b^{2}=16 + 25=41\).

Step3: Find the hypotenuse \(c\)

Since \(c^{2}=41\), then \(c=\sqrt{41}\).

Answer:

\(\sqrt{41}\)