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Let ABC be an equilateral triangle, le...

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 -

A

54

B

108

C

48

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B

`y=(sqrt(3)x)/(2),z=(x)/(2)`
Area of `Delta BKN` is 6
`therefore (1)/(2)yz=6 rArr x^(2)=(48)/(sqrt(3))`
Area of `Delta ABC = 6+6+2xy +(1)/(2)(2x)(2x)sin 60^(@)`
`=12+2x(sqrt(3)x)/(2)+2x^(2)(sqrt(3))/(2)`
`=12+2sqrt(3)xx(48)/(sqrt(3)=108`
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