Find the Hypotenuse AC: Right Triangle with Both Legs Equal to 2

To find the hypotenuse $AC$ in the right triangle $ABC$, we will apply the Pythagorean Theorem. The theorem states that the square of the hypotenuse $c$ (which is the side opposite the right angle), is equal to the sum of the squares of the other two sides $a$ and $b$.

Given that side $AB = 2$ and $BC = 2$, we have:

• $a = 2$
• $b = 2$

According to the Pythagorean Theorem, $c^2 = a^2 + b^2$.

Substituting the given values into the theorem:

$c^2 = 2^2 + 2^2$

$c^2 = 4 + 4$

$c^2 = 8$

To solve for $c$, take the square root of both sides:

$c = \sqrt{8}$

Therefore, the length of the hypotenuse $AC$ is $\sqrt{8}$.

Among the given choices, the correct answer is choice 2: $\sqrt8$.