If you draw a line between the vertex above the side with length 6 straight across and perpendicular to the opposite side, you can create a rectangle, and that line would have a length of 10 because it is congruent with the length of the base.
You can see that the line that you drew in divides the left side of the figure with length 10 into two different lines. You can subtract 6 from 10 to get the length of the upper portion of the line, which is 4.
Knowing these lengths, you can use the Pythagorean theorem to find x. 4^2 + 10^2 = c^2
c = 2 times the square root of 29