https://file.aiquickdraw.com/mathbot/file/17274742377435ppznpb6.jpg

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.

Find the length of the third side. If necessary, write in simplest radical form.

Learn how to find the hypotenuse of a right triangle given the lengths of the other sides using the Pythagorean Theorem. This problem involves applying the theorem and simplifying radicals, suitable for students in Grades 8-10.

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