Question

what is the length of the hypotenuse of the triangle below? a. 9\sqrt{2} b. 1 c. 9 d. 18 e. 81\sqrt{2} f. 18\sqrt{2}

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle with legs \(a\) and \(b\) and hypotenuse \(h\), \(h^{2}=a^{2}+b^{2}\). Here \(a = 9\sqrt{2}\) and \(b = 9\sqrt{2}\).
So \(h^{2}=(9\sqrt{2})^{2}+(9\sqrt{2})^{2}\).

Step2: Calculate squares

\((9\sqrt{2})^{2}=9^{2}\times(\sqrt{2})^{2}=81\times2 = 162\). Then \(h^{2}=162 + 162=324\).

Step3: Find the hypotenuse

Take the square - root of both sides. \(h=\sqrt{324}=18\).

Answer:

D. 18