Directions (38-40): Study the information carefully and answer the questions given below.

Rohit is standing at point A and wants to reach point E. He can only move in a straight line, but there are obstacles in his path. Rohit first moves 4 km towards the north and reaches point B. From there, he turns left and moves 3 km towards the west and reaches point C. He then turns left again and moves 5 km towards the south and reaches point D. Finally, he turns right and moves 8 km and reaches point E. Sonia wants to travel from point E to point A, but there is an additional obstacle in her path. There is a mountain between points E and A, which she cannot cross. Sonia first moves 5 km towards the south from point E and reaches point F. From there, she turns right and moves 6 km and reaches point G. She then turns left and moves 7 km towards the south and reaches point H. Finally, she turns right and moves 3 km and reaches point I. From point I, Sonia needs to reach point A, with shortest distance.

What is the total distance Rohit needs to travel from point A to point G?

The correct option is 31 km.

To find the total distance Rohit needs to travel from point A to point G, let us trace both Rohit's and Sonia's movements step-by-step to determine the layout of all the points.

Step 1: Trace Rohit's path from point A to point E
Let point A be the starting point, which we can assign coordinates $\left(0,0\right)$.
1. Rohit moves 4 km towards the north to reach point B.
Coordinates of B: $\left(0,4\right)$.
2. From B, he turns left (west) and moves 3 km to reach point C.
Coordinates of C: $\left(-3,4\right)$.
3. From C, he turns left (south) and moves 5 km to reach point D.
Coordinates of D: $\left(-3,4-5\right)=\left(-3,-1\right)$.
4. From D, he turns right (west, since he was facing south) and moves 8 km to reach point E.
Coordinates of E: $\left(-3-8,-1\right)=\left(-11,-1\right)$.

Step 2: Trace Sonia's path from point E to point G
Sonia starts from point E $\left(-11,-1\right)$.
1. Sonia moves 5 km towards the south from point E to reach point F.
Coordinates of F: $\left(-11,-1-5\right)=\left(-11,-6\right)$.
2. From F, she turns right (west, since she was facing south) and moves 6 km to reach point G.
Coordinates of G: $\left(-11-6,-6\right)=\left(-17,-6\right)$.

Step 3: Calculate the total distance Rohit travels from A to G
We need to find the distance along the path Rohit would take to go from point A to point G by following the established network of points. Rohit goes from A to B to C to D to E to F and finally to G.
The segments and their lengths are:
- A to B: 4 km
- B to C: 3 km
- C to D: 5 km
- D to E: 8 km
- E to F: 5 km
- F to G: 6 km

Summing these individual distances:
$\text{Total Distance}=4+3+5+8+5+6$
$\text{Total Distance}=31\text{km}$

Therefore, the total distance Rohit needs to travel from point A to point G is 31 km.