Question

Ravi walks 8 km North East and then 6 km Southeast find the total distance as well as shortest distance between starting and ending points a)14,12 km b)14,10 km c)10,8 km d)8,6 km​

Answer 1

Answer:

b)14,10 km

Explanation:

Please refer to the picture attached.

Distance=Actual distance traveled from starting point to finishing point

∴Distance=8+6=14 km

Displacement=Shortest distance between the starting point and end point

Here,the shortest distance between the starting point and end point is the hypotenuse of the right angled triangle.

∴By Pythagoras theorem,we get

                   Displacement=$\sqrt{8^2+6^2}$=$\sqrt{64+36} =\sqrt{100} =10$

Answer 2

Given:

Ravi walks 8km towards NorthEast and then he walks 6km towards SouthEast.

To Find:

The shortest distance between the initial point and the final point. The total distance covered by Ravi.

Solution:

1. It is given that Ravi initially walks a distance of 8 km towards North East. Hence, the total distance covered by Ravi as of now is equal to 8 kilometers.

2. Ravi now walks a distance of 6km towards SouthEast. Hence, the total distance covered during the journey = 8 + 6 - 10 kilometers.

3. When Ravi turned towards SouthEast it is clear that Ravi has turned about 90 degrees. Hence distance walked by Ravi in the two directions is perpendicular to each other.

4. Consider the distance walked by Ravi in two directions as two sides of a triangle. Since the directions are perpendicular, the triangle is right-angled.

5. The shortest distance between the two points = the length of the hypotenuse of the right-angled triangle.

6. The length of hypotenuse =$\sqrt{altitude^{2} +base^{2} }$,

=> Substitute the values 8, 6 in the above formula,

=> Hypotenuse = shortest distance = √100 Km.

=> Shortest distance = 10Km.

Therefore, the shortest distance, the total distance between the two points is 10, 14 kilometers respectively. Option A is the correct answer.