Question

choose the correct values for x and y in the right triangle. x = 12\sqrt{2} y = 24 y = 12\sqrt{2} x = 12

Explanation:

Step1: Identify the triangle type

It's a 45 - 45- 90 right - triangle. In a 45 - 45- 90 triangle, the legs are equal. Given one leg is 12, so $x = 12$.

Step2: Use the Pythagorean theorem or ratio

The ratio of the sides in a 45 - 45- 90 triangle is $a:a:a\sqrt{2}$, where $a$ is the length of a leg and $a\sqrt{2}$ is the hypotenuse. Since $a = 12$, the hypotenuse $y=12\sqrt{2}$.

Answer:

$x = 12$, $y = 12\sqrt{2}$