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A person travels 7 km eastwards and then turns right and travels 3 km and further turns right and travels 13 km. What is the shortest distance of the present position of the person from his starting point?
- a)6 km
- b)3√5 km
- c)7 km
- d)4√5 km
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A person travels 7 km eastwards and then turns right and travels 3 km ...
In triangle ABC
BC = 13 – 7 = 6 km
AB = 3 cm
AC2 = BC2 + AB2 [∵ Pythagoras theorem]
⇒ 62 + 32 = 45
∴ AC = 3√5 km is the shortest distance
BC = 13 – 7 = 6 km
AB = 3 cm
AC2 = BC2 + AB2 [∵ Pythagoras theorem]
⇒ 62 + 32 = 45
∴ AC = 3√5 km is the shortest distance
Most Upvoted Answer
A person travels 7 km eastwards and then turns right and travels 3 km ...
To find the shortest distance from the present position to the starting point, we can draw a right triangle with the legs representing the distances traveled in the eastward and northward directions.
The eastward distance traveled is 7 km, and the northward distance traveled is 3 km. Using the Pythagorean theorem, we can find the hypotenuse, which represents the shortest distance from the present position to the starting point.
Using the Pythagorean theorem:
Hypotenuse^2 = (Eastward distance)^2 + (Northward distance)^2
Hypotenuse^2 = 7^2 + 3^2
Hypotenuse^2 = 49 + 9
Hypotenuse^2 = 58
Taking the square root of both sides, we find:
Hypotenuse ≈ √58 ≈ 7.62
Therefore, the shortest distance of the present position of the person from his starting point is approximately 7.62 km.
The closest answer choice is b) 3 km, but this is not the correct answer.
The eastward distance traveled is 7 km, and the northward distance traveled is 3 km. Using the Pythagorean theorem, we can find the hypotenuse, which represents the shortest distance from the present position to the starting point.
Using the Pythagorean theorem:
Hypotenuse^2 = (Eastward distance)^2 + (Northward distance)^2
Hypotenuse^2 = 7^2 + 3^2
Hypotenuse^2 = 49 + 9
Hypotenuse^2 = 58
Taking the square root of both sides, we find:
Hypotenuse ≈ √58 ≈ 7.62
Therefore, the shortest distance of the present position of the person from his starting point is approximately 7.62 km.
The closest answer choice is b) 3 km, but this is not the correct answer.
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