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

Let hypotenuse = $c$, legs $a=12$, $b=12$.
$$c^2 = a^2 + b^2$$

Step2: Substitute values and calculate

$$c^2 = 12^2 + 12^2 = 144 + 144 = 288$$

Step3: Solve for hypotenuse

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

Answer:

D. $12\sqrt{2}$ cm