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NTA Abhyas JEE Main2020MathematicsStraight LinesPractice

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

Options

  1. A4 : 1
  2. B2 : 1
  3. C8 : 3
  4. D7 : 3

Correct answer

C. 8 : 3

Step-by-step solution

Let the coordinates of the vertices O , P , Q , R be 0 , 0 , a , 0 , a , a , 0 , a , respectively. Then, we get the coordinates of M as a , a 2 and those of N as a 2 , a Therefore, area of ∆ O M N is 1 2 0 0 1 a a 2 1 a 2 a 1 = 3 a 2 8 Area of the square is a 2 . Hence, the required ratio is 8 : 3

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