Directions: Study the given information carefully and answer the question that follows.

Maya starts moving from point A towards the west for 11m to reach point B. Then, she turns right and walks for 4m to reach point C. Then she again turns right and walks for 14m to reach point D and then finally she turns towards south and walks for 6m to reach point E.

Neil starts walking towards north for 2m from point A to reach point F. Then, he takes a right turn and a left turn, walking for 6m and 9m to reach points G and H respectively. Then, he takes a left turn and walks for 5m to reach point I.

What is the shortest distance between point B and point D?

The correct answer is $2\sqrt{53}$ m.

Step 1: Trace Maya's path and determine the coordinates of points B, C, and D.
Let point A be the reference origin (0, 0).
- Point B: Maya starts at point A and moves 11 m West. Therefore, point B is located 11 m West of point A, at coordinates (-11, 0).
- Point C: From point B, she turns right (facing North) and walks 4 m. Therefore, point C is located at (-11, 4).
- Point D: From point C, she turns right again (facing East) and walks 14 m. Adding 14 m to the x-coordinate (-11 + 14 = 3), point D is located at (3, 4).

Step 2: Calculate the shortest distance between point B and point D.
Since Maya turned right at point C (turning from North to East), the angle between path BC and path CD is 90°.
Thus, points B, C, and D form a right-angled triangle ΔBCD with the right angle at vertex C.

The lengths of the two perpendicular sides of ΔBCD are:

Side BC = 4 m

Side CD = 14 m

Using the Pythagoras theorem, the shortest distance (hypotenuse BD) is:

$BD=\sqrt{{BC}^2+{CD}^2}$

Substitute the given values into the formula:

$BD=\sqrt{4^2+{14}^2}$

$BD=\sqrt{16+196}$

$BD=\sqrt{212}$

Simplifying the radical expression:

$BD=\sqrt{4\times 53}=2\sqrt{53}\text{m}$

Hence, the shortest distance between point B and point D is $2\sqrt{53}$ m.