Tower A is $90$ m tall and tower B is $140$ m tall. They are 100 m apart. A horizontal skywalk connects the floors at $70$ m in both the towers. If a taut rope connects the top of tower A to the bottom tower B, at what distance (in meters) from tower A will the rope intersect the skywalk?

- $22.22$
- $50$
- $57.87$
- $77.78$