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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


Team Careers360 2nd Jan, 2024
Answer (1)
Team Careers360 11th Jan, 2024

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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