Question

Please help this is for a big grade

Answer 1

x = 12

Side length =
`2√(3)` in

Explanation:

Area of the given hexagon = 6 × (Area of the triangular section)

Area of the triangular section =
`(1)/(2)(\text{Base})(\text{Height})`

=
`(1)/(2)(2)(√(3))^{(x)/(12)}(√(3))^{(x)/(6)}`

=
`(√(3))^{(x)/(12)}[(√(3))^2]^{(x)/(12)}`

=
`(√(3))^{(x)/(12)}(3)^{(x)/(12)}`

=
`(3√(3))^{(x)/(12)}`

Now area of the given hexagon =
`6(3√(3))^{(x)/(12)}`

Since, area of the hexagon is =
`18√(3)` in²

`6(3√(3))^{(x)/(12)}=18√(3)`

`(3√(3))^{(x)/(12)}=(3√(3))^1`

`(x)/(12)=1`

x = 12

Therefore, side length =
`2(√(3))^{(x)/(12)}`

=
`(2√(3))^{(12)/(12)}`

=
`2√(3)` in.