Question

choose the correct values for x and y in the right triangle. select all correct options y = 9 y = 9\sqrt{2} x = 18 x = 9\sqrt{2}

Explanation:

Step1: Identify triangle type

This is a 45 - 45 - 90 right - triangle. In a 45 - 45 - 90 triangle, the ratio of the sides is $1:1:\sqrt{2}$. If the length of a leg is $a$, the other leg has length $a$ and the hypotenuse has length $a\sqrt{2}$.

Step2: Find the value of $y$

Since the non - hypotenuse sides of a 45 - 45 - 90 triangle are equal, and one leg is 9, then $y = 9$.

Step3: Find the value of $x$

The hypotenuse $x$ of a 45 - 45 - 90 triangle with leg length $a = 9$ is given by $x=a\sqrt{2}=9\sqrt{2}$.

Answer:

$y = 9$, $x = 9\sqrt{2}$