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AP EAMCET2011MathematicsProperties of Triangles

In a A B C , if a ^2 C 2 +c ^2 A 2 = 3 b 2 , then the sides of the triangle are in

Options

  1. Aan arithmetic progression
  2. Ba geometric progression
  3. Ca harmonic progression
  4. Dan arithmetico-geometric progression

Correct answer

A. an arithmetic progression

Step-by-step solution

In A B C, a ^2 c 2 +a ^2 A 2 = 3 b 2 array lc & a s(s-c) a b ^2+c s(s-a) b c = 3 b 2 & a s(s-c) a b +c s(s-a) b c = 3 b 2 & s(s-c) b + s(s-a) b = 3 b 2 & s b (s-c+s-a)= 3 b 2 & 2 s(2 s-a-c)=3 b^2 & 2 s(a+b+c-a-c)=3 b^2 & [ 2 s=a+b+c] & 2 s b=3 b^2 & 2 s=3 b & a+b+c=3 b & 2 b=a+c array a, b, c are in arithmetic progression.

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