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 from the bottom of both towers. If a taut rope connects the top of Tower A to the bottom of Tower B, at what distance (in meters) from Tower A will the rope intersect the skywalk?

GATE 2018 · General Aptitude · Geometry · medium

Answer: Distance from Tower A = 200/9 ≈ 22.22 m

1. Set up coordinates: Place Tower A at the origin. Top of A = (0, 90). Bottom of B = (100, 0).
2. Equation of the rope (line from A-top to B-bottom): y = 90 - (9/10)x
3. Substitute skywalk height y = 70: x = 200/9 ≈ 22.22 m