There are 2 congruent right triangles in this trapezoid. The hypotenuse and adjacent side lengths are 19 and 17 respectively. Using the Pythagorean Theorem, 19^2-17^2 is 72. The square root of 72 is approximately 8.48528137424. That is the length of the portions on the bottom that don't include the length x. 8.48528137424*2 is approximately 16.9705627485. 31-16.9705627485 gives you the length of the side x.
