Question

what is the length of the hypotenuse? 6 cm (not drawn to scale) a 3 cm b 9 cm c 45 cm d 3√5 cm

Explanation:

Step1: Apply Pythagorean theorem

Let \(a = 3\) cm and \(b=6\) cm. The Pythagorean theorem for a right - triangle is \(c^{2}=a^{2}+b^{2}\), where \(c\) is the hypotenuse. So \(c^{2}=3^{2}+6^{2}\).

Step2: Calculate the squares

\(3^{2}=9\) and \(6^{2}=36\), then \(c^{2}=9 + 36=45\).

Step3: Solve for \(c\)

\(c=\sqrt{45}=\sqrt{9\times5}=3\sqrt{5}\) cm.

Answer:

D. \(3\sqrt{5}\) cm