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 \(a = 12\), \(b = 12\), and \(c\) is the hypotenuse.
$$c^{2}=12^{2}+12^{2}$$

Step2: Calculate \(c^{2}\)

$$c^{2}=144 + 144=288$$

Step3: Solve for \(c\)

$$c=\sqrt{288}=\sqrt{144\times2}=12\sqrt{2}$$

Answer:

\(12\sqrt{2}\text{ cm}\) (the fourth option)