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
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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