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Easy

Question

If the sides of a triangle ABC are a, b and c such that 2b = a + c,blankthen exhaustive range of fraction numerator b over denominator c end fraction is

  1. open parentheses fraction numerator 2 over denominator 3 end fraction comma 2 close parentheses    
  2. left parenthesis 01 right parenthesis    
  3. open parentheses negative fraction numerator 1 over denominator 2 end fraction comma 2 close parentheses    
  4. left parenthesis 46 right parenthesis    

The correct answer is: open parentheses fraction numerator 2 over denominator 3 end fraction comma 2 close parentheses


    a + b > c
    Adding c to both sides, we get
    3 b greater than 2 c rightwards double arrow fraction numerator b over denominator c end fraction greater than fraction numerator 2 over denominator 3 end fraction
    N o w comma
    b plus c greater than a rightwards double arrow b plus c greater than 2 b minus c
    text and  end text 2 c greater than b rightwards arrow fraction numerator b over denominator c end fraction less than 2
    Therefore,
    fraction numerator b over denominator c end fraction element of open parentheses fraction numerator 2 over denominator 3 end fraction comma 2 close parentheses

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