A person starts walking in south and after walking 20 meter he took a left turn and walks 30 meter and finally took a right turn and stopped after walking 40 meters. Find the distance between his initial position to final position?
Answers
Answer:
90
Step-by-step explanation:
20+30=50
50+40=90
I HOPE IT IS CORRECT
- The distance between person's initial position to final position is equal to 30√5 m .
Given :- A person starts walking in south and after walking 20 meter he took a left turn and walks 30 meter and finally took a right turn and stopped after walking 40 meters.
To Find :- The distance between his initial position to final position ?
Solution :- { Refer to image for diagram }
Case 1) :-
- Let initial position = Point A .
- From point A he walks 20 m towards south and reach at point B .
- AB = 20 m .
Case 2) :-
- From point B he turns left , towards east direction and walks 30 m and reach at point C .
- BC = 30 m
Case 3) :-
- From point C he turns right , towards south direction and walks 40 m and reach at point D and stopped .
- CD = 40 m
- Final position = point D .
from image we can see that,
→ CD = BE = 40 m
and,
→ BC = ED = 30 m
therefore, in right angled ∆AED we have,
→ AE = AB + BE = 20 + 40 = 60 m
→ ED = 30 m { Equals to BC }
So,
→ AD² = AE² + ED² { By pythagoras theorem }
→ AD² = (60)² + (30)²
→ AD² = 3600 + 900
→ AD² = 4500
square root both sides,
→ AD = √(4500)
→ AD = √(900 × 5)
→ AD = √(30² × 5)
→ AD = 30√5 m (Ans.)
Hence, the distance between his initial position to final position is equal to 30√5 m .
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