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: Apply Pythagorean theorem

In a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(a\) and \(b\) are the legs and \(c\) is the hypotenuse. Here \(a = 12\) and \(b=12\).

Step2: Substitute values

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

Step3: Solve for \(c\)

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

Answer:

\(12\sqrt{2}\text{ cm}\)