We are given a right triangle with one side length 6 and the hypotenuse $2\sqrt{13}$. We need to find the length of the other side.

1. Problem Description

We are given a right triangle with one side length 6 and the hypotenuse $2\sqrt{13}$. We need to find the length of the other side.

2. Solution Steps

Let the unknown side be $x$. Since we have a right triangle, we can use the Pythagorean theorem:

$a^2 + b^2 = c^2$, where $a$ and $b$ are the legs and $c$ is the hypotenuse.

In this case, we have:

$6^2 + x^2 = (2\sqrt{13})^2$

$36 + x^2 = 4 * 13$

$36 + x^2 = 52$

$x^2 = 52 - 36$

$x^2 = 16$

$x = \sqrt{16}$

$x = 4$

3. Final Answer

4