A boy started cycling towards the west. He cycled for 3 km, then he took a 450 right turn and cycled for 3V2km, then he turned 45° left and cycled for 2 km and finally he turned left and cycled another 3 km. From this point, what is the
shortest distance to his starting point?
Pick ONE option
A) 9 km
B) 10 km
A
C) 8 km
D) 9.5 km
Answers
Answer:
The answer is C) 8KM Ok Friend
The shortest distance from starting point is 8km.
Let us say the boy cycled 3km from point A to point B westwards. Then he took a 45° right turn and cycled for 3√2 km to point C. Then he turned 45° left and cycled for 2km to point D. Then finally turned left 90° and cycled 3 km to point E.
∴ We get the length of the hypotenuse of triangle BCF as 3√2 km and one angle ∠CBF as 45°.
Therefore, solving for side length as both sides are equal,
Side²= 18 ÷ 2
Side = 3 km
As he travelled along path DE parallel to the direction of side CF as shown in figure,
He actually travelled to a position situated in a straight line from the starting point.
Hence, distance CD = FE
∴ FE = 2km
Hence, shortest distance from starting point = AB + BF + FE
= 3+3+2
= 8km
