Anju starts from Lucknow and drives 18 km towards west. She then takes a right turn, drives 14 km, turns right again and drives 9 km. She takes a final right turn, drives 2 km and stops at Point F. What is the shortest distance between Point F and Lucknow?

Let Anj u's starting point be A.
She drives 18 km west and reaches C.
She turns right and travels 14 km to reach D.
Then she turns right again and travels 9 km to reach E.
Finally, she turns right and travels 2 km to reach F.

We need to find the shortest distance from A to F.

Since Anju only takes 90-degree turns, the triangle ABF is a right triangle right-angled at B.

AB = AC - CB

CB = DE = 9

AB = 18 - 9 = 9

BF = BE - EF = CD - EF = 14 - 2 = 12

$$\ AF=\sqrt{\ 9^2+12^2}=15$$

Hence, the shortest distance of point F and Lucknow is 15 km.