Let ABC be an equilateral triangle, let KLMN be a rectangle with K, L on BC , M on AC and N on AB. Suppose `AN//NB = 2` and the area of triangle BKN is 6. The area of the triangle ABC is -

Options

A. 54
B. 108
C. 48
D. not determinable with the above data

Answer

B

Explanation

`y = (sqrt(3)x)/(2)`
`z = x/2`
`1/2 yz =6 rArr x^(2) = (48)/(sqrt(3))`
Area of `DeltaABC = 6 + 6 + 2xy + 1/2 (2x)(2x) sin 60^(@)`
` = 12 + 2x (sqrt(3x))/(2) + 2x^(2) (sqrt(3))/(2)`
`12 + 2sqrt(3) xx (48)/(sqrt(3)) = 108`