A truck leaves a depot and goes 5 km towards the East. It turns right and goes 27 km, turns right again and goes 25 km, and then turns right once more and goes 6 km. What is the shortest distance between the truck and the depot now?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 29 km
A right turn moves the facing direction one step clockwise (East → South → West → North). Keep a running total of the distance east (or west) and north (or south) of the depot; then use Pythagoras.
Facing East, 5 km: 5 km east of the depot
Turns right, now facing South, 27 km: 5 km east, 27 km south
Turns right, now facing West, 25 km: \(25-5=20\) km west, 27 km south
Turns right, now facing North, 6 km: 20 km west, \(27-6=21\) km south
Shortest distance \(=\sqrt{20^{2}+21^{2}}=\sqrt{400+441}=\sqrt{841}=29\) km
The shortest distance is 29 km.
