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AP EAMCET202317 May 2023Morning ShiftMathematicsProperties of TrianglesActual

In ABC , A , B and C are in arithmetic progression and a: c=1: 2 . If b=4 3 ~cm , then the area of A B C (in sq. cm ) is

Options

  1. A16 3
  2. B12 3
  3. C8 3
  4. D6 3

Correct answer

C. 8 3

Step-by-step solution

A, B, C are in A.P. 2 B=A+C Now, A+B+C= 3 ~B = B= 3 Now, (C-A) 2 = c-a c+a ( B 2 )= c a -1 c a +1 ( 6 )= 2-1 2+1 3 = 1 3 3 = 1 3 C-A 2 = 6 C-A= 3 ....(i) Also, A+C=2 B= 2 3 ...(ii) Solving (i) & (ii) C= 2 Now, a^2+b^2=c^2 a^2+48=c^2 b=4 3 a^2 c^2 + 48 c^2 =1 1 4 - 48 c^2 =1 c=8 a c = 1 2 a=4c 2 Now, area of triangle = 1 2 a b= 1 2 4 4 3 =8 3

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