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…

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})