The distance from F to G on walkway C is approximately 259.81 meters, which is closest to option A, 360 meters.
Based on the given information, the distance from F to G on walkway C is 150 meters. The map shows that walkway A and walkway B are parallel, and walkway C intersects them at a right angle. Therefore, we can use the Pythagorean theorem to find the distance from F to G:
FG² = FC² + CG²
Since walkway C intersects walkway A at a right angle, we can use the Pythagorean theorem to find the length of FC:
FC² = FA² + AC²
Since walkway A and walkway B are parallel, we know that AC = BG. Also, since walkway A and walkway C intersect at a right angle, we can use the Pythagorean theorem to find the length of FA:
FA² = AC² + CF²
Substituting AC = BG and simplifying, we get:
FA² = BG² + CF²
Since walkway B and walkway C are parallel, we know that CG = BG. Substituting AC = BG and CG = BG, we get:
FC² = BG² + CF²
Now, we can substitute FC² and CG² into the first equation:
FG² = (BG² + CF²) + BG²
Simplifying, we get:
FG² = 2BG² + CF²
Taking the square root of both sides, we get:
FG = sqrt(2BG² + CF²)
Substituting BG = 150 meters and CF = 100 meters, we get:
FG = sqrt(2(150²) + 100²) = sqrt(45000) = 150sqrt(3)
Therefore, the distance from F to G on walkway C is approximately 259.81 meters, which is closest to option A, 360 meters.