Question : Directions: Pratima departs from her house and walks 29 m towards the north, then turns right and walks 16 m. Now she turns right again and walks 17 m. She again, takes a right turn and stops after walking for 21 m. What is the shortest distance between Pratima and her house now? (Assuming that all turns are 90-degree turns only.)
Option 1: 17 m
Option 2: 18 m
Option 3: 13 m
Option 4: 12 m
Correct Answer: 13 m
Solution : First, we will draw the diagram, as per the given instructions –
Here, A is the starting point and F is the finishing point.
AB = 29 m; BC = DE = 16 m; CD = BE = 17 m; DF = 21 m
And, AE = AB – BE
AE = 29 – 17
AE = 12 m
EF = DF – DE
EF = 21 – 16
EF = 5 m
By applying the Pythagorean theorem –
(AF)
2
= (AE)
2
+ (EF)
2
(x)
2
= (12)
2
+ (5)
2
= 144 + 25 = 169
⇒ AF = $\sqrt{169}$ = 13 m
So, the shortest distance between Pratima and her house is 13 m. Hence, the third option is correct.
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