Question

what is the length of the hypotenuse of the triangle below? 45° 3√2 h 90° 45° 3√2 a. 9√2 b. 3 c. 6 d. 1 e. 6√2 f. 3√2

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, the Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse and \(a\) and \(b\) are the legs. Here \(a = 3\sqrt{2}\) and \(b = 3\sqrt{2}\).
So, \(c^{2}=(3\sqrt{2})^{2}+(3\sqrt{2})^{2}\).

Step2: Calculate \((3\sqrt{2})^{2}\)

\((3\sqrt{2})^{2}=3^{2}\times(\sqrt{2})^{2}=9\times2 = 18\).
Then \(c^{2}=18 + 18\).

Step3: Find \(c^{2}\) and \(c\)

\(c^{2}=36\), so \(c=\sqrt{36}=6\).

Answer:

C. 6