The triangle in the image is a right triangle with one leg of length $2$ and another leg of length $2\sqrt{3}$. To find the length of the third side (the hypotenuse), we can apply the Pythagorean Theorem:

$a^2 + b^2 = c^2$

where $a$ and $b$ are the lengths of the legs, and $c$ is the hypotenuse.

Let's substitute the values:

• $a = 2$
• $b = 2\sqrt{3}$

$(2)^2 + (2\sqrt{3})^2 = c^2$

Now, let's solve for $c$.

$4 + 4(3) = c^2$ $4 + 12 = c^2$ $16 = c^2$ $c = \sqrt{16} = 4$

Thus, the length of the hypotenuse is $4$.

Would you like more details or have any questions? Here are some related problems you might find helpful:

1. How do you apply the Pythagorean Theorem to non-integer values?
2. What is the relationship between the sides of a 30-60-90 triangle?
3. How do you simplify square roots like $2\sqrt{3}$?
4. What are common mistakes when solving right triangle problems?
5. How do you determine when a triangle is a right triangle given three sides?

Tip: When using the Pythagorean Theorem, always simplify square roots to their simplest radical form to avoid calculation errors.