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KVPY2010MathematicsProperties of Triangles

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

  1. A54
  2. B108
  3. C48
  4. Dnot determinable with the above data

Correct answer

B. 108

Step-by-step solution

y= 3 x 2 z= x 2 1 2 y z=6 x²= 48 3 Area of ABC =6+6+2 xy + 1 2 (2 x )(2 x ) 60^ =12+2 x 3 x 2 +2 x ² 3 2 12+2 3 48 3 =108

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