Question : Directions: Mohan’s house faces south. He steps out of his house and goes straight for 30 m. From there, he takes two successive right turns and covers a distance of 6 m and 24 m, respectively. Finally, he takes a left turn and walks a distance of 2 m to reach a grocery shop. What is the shortest distance between his house and the grocery shop?
Option 1: 12 m
Option 2: 6 m
Option 3: 8 m
Option 4: 10 m
Correct Answer: 10 m
Solution : Firstly, we will draw the diagram as per the given instructions –
Here, A is the starting point (Mohan's house), and E is the endpoint (Grocery shop).
AB = 30 m; BC = 6 m; CD = 24 m; DE = 2 m;
OD = BC = 6 m; OB = DC = 24 m
OE = OD + DE = 6 + 2 = 8 m; OA = AB – OB = 30 – 24 = 6 m
By applying the Pythagoras theorem –
(AE)
2
= (OE)
2
+ (OA)
2
(AE)
2
= (8)
2
+ (6)
2
= 64 + 36 = 100
⇒ AE = $\sqrt{100}$ = 10 m
So, the shortest distance between Mohan's house and the grocery shop is 10 m. Hence, the fourth option is correct.
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