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If center of a regular hexagon is at the origin and one of the vertices on the Argand diagram is `1+2i` , then its perimeter is `2sqrt(5)` b. `6sqrt(2)` c. `4sqrt(5)` d. `6sqrt(5)`

A

`2sqrt(5)`

B

`6sqrt(5)`

C

`4sqrt(5)`

D

`6sqrt(5)`

Text Solution

Verified by Experts

The correct Answer is:
D

Let the vertices be `z_(0),z_(1),…….,z_(5)` w.r.t centre O at origin and `|z_(0)|= sqrt(5)`
Now `DeltaOA_(2)A_(3)` is equilateral
`rArr OA_(2) = OA_(3) =A_(2)A_(3) =sqrt(5)`
Perimeter `= 6sqrt(5)`
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