Question

A park has the shape of a regular hexagon of sides 2 m each. Ram walks a distance of 5 m around the perimeter. What is the direct distance between the start point and the end point?

• A.
• B.
  
• C.
  
• D.
  

Answer 1

The correct option is B

Vertex angle for regular hexagon = $\frac{{180}^{\circ }(6-2)}{6}={30}^{\circ }\times 4={120}^{\circ }$

In the $\Delta$ABC, $\angle$ACB = $\angle$CAB = 30${}^{\circ }$

We know 30${}^{\circ }$ - 60${}^{\circ }$ - 90${}^{\circ }$ = 1 : $\sqrt{3}$ : 2 ; AC = 2$\sqrt{3}$
Now, from $\Delta$ACD:-
1${}^2$ + $(2\sqrt{3}{)}^2$ = AD${}^2$;AD = $\sqrt{13}$.Option (b)
The starting point of Ram is A and end point is D.
Alternate Solution:
The answer option will have to be between 2$\sqrt{3}$ and 4 i.e. between $\sqrt{12}$ and $\sqrt{16}$.

Only option (b) fulfils the given condition and hence option (b) is the correct answer choice.