Ravi walked 2 km towards the South, took a right turn and walked 3 km. Then he took a left turn and walked 2 km. At what distance is he now from the starting point?Options2 km6 km4 km5 km
Question
Ravi walked 2 km towards the South, took a right turn and walked 3 km. Then he took a left turn and walked 2 km. At what distance is he now from the starting point?Options2 km6 km4 km5 km
Solution
Ravi's total distance travelled can be visualized as a right-angled triangle.
- He first walked 2 km south.
- Then he took a right turn and walked 3 km. This means he is now walking west.
- Then he took a left turn and walked 2 km. This means he is now walking south again.
So, he has walked 2 km south, 3 km west, and then 2 km south again.
The distance from his starting point is not simply the sum of these distances, because he did not walk in a straight line. Instead, we need to find the hypotenuse of the right-angled triangle formed by his 3 km walk west and his total 4 km walk south (2 km initially and then 2 km after the left turn).
We can use the Pythagorean theorem to find this distance. The theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
So, the distance from his starting point is sqrt((3 km)^2 + (4 km)^2) = sqrt(9 km^2 + 16 km^2) = sqrt(25 km^2) = 5 km.
So, Ravi is 5 km away from his starting point.
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