Find the value of x on the figure below.

Based on the triangles formed by the vertical lines on the figure, we can see that the ratio of the length of the longer segment to the shorter segment is 2:1. We already know that the shorter segment has a length of 2x, so the longer segment must have a length of 4x. Next, we can apply the Pythagorean theorem to the right triangle on the left side of the figure. We have: (2x)^2 + 6^2 = (4x)^2 Simplifying this equation gives: 4x^2 + 36 = 16x^2 Subtracting 4x^2 from both sides gives: 36 = 12x^2 Dividing both sides by 12 gives: 3 = x^2 Taking the square root of both sides gives: x = ±?3 However, since we are dealing with a length, we can discard the negative solution. Therefore, the value of x is ?3.