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AP EAMCET201824 Apr 2018Morning ShiftMathematicsProperties of TrianglesActual

In a triangle, if the ex-radii r₁, r₂, r₃ are in the ratio 1: 2: 3 , then its sides are in the ratio

Options

  1. A5: 8: 9
  2. B5: 4: 3
  3. C7: 9: 11
  4. D1: 2: 3

Correct answer

A. 5: 8: 9

Step-by-step solution

Given that, r₁, r₂, r₃ are ex-radii of triangle and aligned & r₁: r₂: r₃=1: 2: 3 & r₁=x, r₂=2 x, r₃=3 x aligned On adding Eqs. (i), (ii) and (iii), we get gathered 3 s-(a+b+c)= x + 2 x + 3 x s= 11 6 x gathered From Eqs. (i), (ii), (iii), we get a= 5 6 x , b= 8 6 x , c= 9 6 x So, a: b: c=5: 8: 9 .

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