Question

each leg of a 45° - 45° - 90° triangle measures 12 cm. what is the length of the hypotenuse? 6 cm 6√2 cm 12 cm 12√2 cm

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle with legs \(a\) and \(b\) and hypotenuse \(c\), \(a^{2}+b^{2}=c^{2}\). Here \(a = 12\) cm and \(b = 12\) cm.

Step2: Substitute values into the formula

\(c^{2}=12^{2}+12^{2}=144 + 144=288\).

Step3: Solve for \(c\)

\(c=\sqrt{288}=\sqrt{144\times2}=12\sqrt{2}\) cm.

Answer:

D. \(12\sqrt{2}\) cm