Question

what is the length of the hypotenuse of a right triangle with legs that are 4 and 9 units long, respectively?
36
18
√97
13
√13
question help: video
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Explanation:

Step1: Recall Pythagorean theorem

Let \(a = 4\), \(b=9\), and the hypotenuse be \(c\). The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\).

Step2: Substitute values

Substitute \(a = 4\) and \(b = 9\) into the formula: \(4^{2}+9^{2}=c^{2}\), so \(16 + 81=c^{2}\), and \(c^{2}=97\).

Step3: Solve for \(c\)

Take the square - root of both sides. Since \(c>0\) (length), \(c=\sqrt{97}\).

Answer:

C. \(\sqrt{97}\)