In a large level rectangular field a tall wooden tower was built for training parachute jumpers. The tower is in the shape of a truncated rectangular pyramid. That is, the base is a rectangle, and the top is a smaller rectangle parallel to the base. The longer sides of the field, the base of the tower and the top of the tower are all oriented east to west.

After several years of use, a strong gale tilted the tower, so that the western edge of the top was higher than the eastern edge. (The top was still a rectangle with its eastern and western edges parallel to the eastern and western edges of the field.) The engineers determined that the tower was still fit for use, but to prevent further tilting they stretched cables tightly from the corners of the field to the nearest corners of the top of the tower. The lengths of these cables, going clockwise are 95, 109, 125, and X meters.

What is X?