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BITSAT2018MathematicsStraight LinesActual

O P Q R is a square and M , N are the middle points of the sides P Q and Q R respectively, then the ratio of the areas of the square and Δ O M N is

Options

  1. A4 : 1
  2. B2 : 1
  3. C8 : 3
  4. D4 : 3

Correct answer

C. 8 : 3

Step-by-step solution

Taking the coordinates of vertices   O ,   P ,   Q ,   R as ( 0 , 0 ) ,   ( a , 0 ) ,   ( a , a ) ,   ( 0 , a ) , respectively. ∴ The coordinates of M is a , a 2 and N is a 2 , a ∴ Area of Δ O M N = 1 2 0 0 1 a a / 2 1 a / 2 a 1 = 3 a 2 8 and area of the square = a 2 ∴ The required ratio is 8 : 3 . Hence, option (c) is correct.

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