Question

each leg of a 45°-45°-90° triangle measures 12 cm. what is the length of the hypotenuse? triangle with vertices z, x, y, right-angled at y, angles at z and x are 45°, legs zy and xy are 12 cm each options: 6 cm, 6√2 cm, 12 cm, 12√2 cm

Explanation:

Step1: Apply Pythagorean theorem

For a right triangle, $c^2 = a^2 + b^2$, where $a,b$ are legs, $c$ is hypotenuse.

Step2: Substitute leg lengths

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

Step3: Solve for hypotenuse

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

Answer:

12$\sqrt{2}$ cm (Option D: $12\sqrt{2}$ cm)