Question

what type of special right triangle is pictured below?
solve for the missing sides.
x =
y =
options: 8√6, 12√3, 2√6, 12, 24, 8√3, 24√2, 12√2

Explanation:

Step1: Identify triangle type

This is a 45-45-90 right triangle (isosceles right triangle), where the two legs are equal, and the hypotenuse is $\text{leg} \times \sqrt{2}$.

Step2: Solve for leg length

Let the legs $x = y$. The hypotenuse is $2\sqrt{6}$. Use the hypotenuse formula:
$$\text{Hypotenuse} = x\sqrt{2}$$
$$2\sqrt{6} = x\sqrt{2}$$
$$x = \frac{2\sqrt{6}}{\sqrt{2}} = 2\sqrt{\frac{6}{2}} = 2\sqrt{3}$$

Step3: Confirm equal legs

Since it is a 45-45-90 triangle, $x = y$, so $y = 2\sqrt{3}$.

Answer:

What type of special right triangle is pictured below? 45-45-90 right triangle
$x = 2\sqrt{3}$
$y = 2\sqrt{3}$