Question : Directions: Rashmi stepped out of her college and walked 15 m towards the South. She then took a left turn and walked 35 m to reach a pastry shop. She then took a right turn and walked 15 m. She then took a right turn and walked 35 m to reach her house. What is the approximate shortest distance between Rashmi's college and her house via the pastry shop?
Option 1: 38 m
Option 2: 69 m
Option 3: 76 m
Option 4: 54 m
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Correct Answer: 76 m
Solution : According to the instructions given, the diagram is as follows –
Now, find the shortest distance between Rashmi's college and her house via the pastry shop –
Here, A is the starting point and E is the finishing point and AE is the total distance from the starting point.
AB = CD = 15m; BC = DE = 35m
By applying the Pythagorean theorem –
(AC)
2
= (AB)
2
+ (BC)
2
(AC)
2
= (15)
2
+ (35)
2
= 225 + 1225 = 1450
⇒ AC = $\sqrt1450$ = 38m = CE
Now, add AC and CE to find the approximate shortest distance between Rashmi's college and her house via the pastry shop –
AC + CE = 38 + 38 = 76m
So, the approximate shortest distance between Rashmi's college and her house via the pastry shop is 76m. Hence, the third option is correct.
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