each leg of a 45° - 45° - 90° triangle measures 12 cm. what is the length of the hypotenuse? 6 cm 6√2 cm 12…

Answer:

D. $12\sqrt{2}\text{ cm}$

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle with legs $a$ and $b$ and hypotenuse $c$, $c^{2}=a^{2}+b^{2}$.

Step2: Identify values of $a$ and $b$

Here $a = 12\text{ cm}$ and $b = 12\text{ cm}$.

Step3: Substitute values into formula

$c^{2}=12^{2}+12^{2}=144 + 144=288$.

Step4: Solve for $c$

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