Olympiad workbookIOQMStraight Lines
An ant leaves the anthill for its morning exercise. It walks 4 feet east and then makes a 160^ turn to the right and walks 4 more feet. It then makes another 160^ turn to the right and walks 4 more feet. If the ant continues this pattern until it reaches the anthill again, what is the distance in feet it would have walked?
Correct answer
36
Step-by-step solution
aligned & Let A₀(0,0) & A₁(4 0,4 0) & A₂(4 0+4 160,4 0+4 160) & A_n=(0,0) & 4( 0+ 160+ . .+ 160(n-1))=0 and 4( 0+ 160+ . .+ 160(n-1))=0 & (80 n)=0 & n = 9 & distance covered =4 9=36 feet aligned