Question

what is the measure of the hypotenuse of a right triangle with side lengths 8 and 5?
√13
√39
√89
√169

Explanation:

Step1: Apply the Pythagorean theorem

For a right - triangle with legs \(a = 8\) and \(b = 5\), and hypotenuse \(c\), the Pythagorean theorem is \(c^{2}=a^{2}+b^{2}\).
So, \(c^{2}=8^{2}+5^{2}\).

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

\(8^{2}=64\) and \(5^{2}=25\). Then \(a^{2}+b^{2}=64 + 25=89\).
Since \(c^{2}=89\), then \(c=\sqrt{89}\) (because \(c>0\) as it is a length).

Answer:

\(\sqrt{89}\) (the third option)