Question

choose the correct values for x and y in the right triangle. select all correct options y = 4√6 x = 4 x = 4√3 y = 8√3

Explanation:

Step1: Identify triangle type

This is a 45 - 45-90 right - triangle. In a 45 - 45-90 triangle, the legs are equal. Given one leg is $4\sqrt{3}$, so $x = 4\sqrt{3}$.

Step2: Use hypotenuse formula

The formula for the hypotenuse $y$ of a 45 - 45-90 triangle is $y=\sqrt{2}\times\text{leg}$. Substituting the leg length $a = 4\sqrt{3}$, we get $y=\sqrt{2}\times4\sqrt{3}=4\sqrt{6}$.

Answer:

$x = 4\sqrt{3}$, $y = 4\sqrt{6}$