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Question : Directions: Diogo’s house faces west. He steps out of his house and walks 22 m straight. He then turns to his left and walks 20 m. He takes another left turn and walks 25 m. Finally, he turns left once again and walks further for 24 m to reach his school. How far is the school from his house and in which direction respect to his house?

Option 1: 5 m due north-east

Option 2: 7 m due north-east

Option 3: 5 m due north-west

Option 4: 25 m due south-east


Team Careers360 3rd Jan, 2024
Answer (1)
Team Careers360 13th Jan, 2024

Correct Answer: 5 m due north-east


Solution : Firstly, we will draw the diagram as per the given instructions –

Here, O is the starting point (Diogo's house), and D is the endpoint (Diogo's school).
AB = 20 m; BC = 25 m; CD = 24 m; OA = 22 m; EC = AB = 20 m
DE = CD – EC = 24 – 20 = 4 m; OE = BC – OA = 25 – 22 = 3 m

By applying the Pythagoras theorem –
(OD) 2 = (DE) 2 + (OE) 2
(OD) 2 = (4) 2 + (3) 2 = 16 + 9 = 25
⇒ OD = $\sqrt{25}$ = 5 m

So, Diogo's school is 5 m from his house in the north-east direction. Hence, the first option is correct.

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