Question

Two army trucks start from same army base, 1st truck travels 11 km south, then turn to left and travel 19 km. 2nd truck travels 11 km west, then turns to its right and travel 5 km. Find the shortest distance between the final positions of both the truck? *

a) 36 km

b) 32 km

c) 17 km

d) 34 km

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Answer 1

Answer:

The shortest distance between the final positions of both the trucks is 34 Km.

Explanation:

Given,

Truck 1 travels 11 Km South. And then travels 19 Km to their left.

Truck 2 travels 11 Km West. And then travels 5 Km to their right.

To find,

The shortest distance between the final positions of both the truck.

Calculation,

For Truck 1

Step (1): Let the truck starts at point 'O' and travel to point 'A' towards South for 11 Km.

Step (2): From point 'A' let the truck travel to point 'B' for 5 Km towards their left, that is 19 km towards the East.

For Truck 2

Step (1): Let the truck starts at point 'O' and travel to point 'P' towards the West for 11 Km.

Step (2): From point 'P' let the truck travel to point 'Q' for 5 Km towards their right, that is 5 km towards the North.

Now the shortest distance is the straight line distance between points B and Q.

Extend the lines PQ and AB so that they meet at O'

Hence, ΔQO'B forms a right-angled triangle, with QO' = 5 km + 11 km = 16 km, and BO' = 19 km + 11 km = 30 Km.

From Pythagoras theorem

O'Q² + O'B² = BQ²

⇒ BQ² = 16² + 30²

⇒ BQ² = 1156

⇒ BQ = 34 km.

Therefore, the shortest distance between the final positions of both the trucks is 34 Km.

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