Question : Directions: Aunt Gloria walked out of her house and walked 65 m towards the east. She took a left turn and walked 28 m. Again, she took a left turn and walked 110 m to reach a public library. How far (shortest distance) and in which direction is the library from Aunt Gloria’s house?
Option 1: 48 m, North-East
Option 2: 48 m, North-West
Option 3: 53 m, North-East
Option 4: 53 m, North-West
Correct Answer: 53 m, North-West
Solution : According to the given instructions the diagram is given below –
Now, find the direction and shortest distance between the house and the public library.
Here, AB = CD = 65 m; BC = AD = 28 m; CE = 110 m;
DE = CE – CD = 110 – 65 = 45 m
The distance (AE) between the house and the public library can be calculated using the Pythagoras Theorem –
(AE)
2
= (AD)
2
+ (DE)
2
(AE)
2
= (28)
2
+ (45)
2
(AE)
2
= 784 + 2025
(AE)
2
= 2809
Squaring on both sides –
AE = 53
So, the shortest distance is 53 m and the public library is in the north-west direction from the house. Hence, the
fourth option
is correct.
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