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AP EAMCET201920 Apr 2019Morning ShiftMathematicsProperties of TrianglesActual

In triangle (A B C ), if ( b+c 9 = c+a 10 = a+b 11 ), then ( A+ B C = )

Options

  1. A( 9 10 )
  2. B( 10 11 )
  3. C( 11 12 )
  4. D( 12 13 )

Correct answer

C. ( 11 12 )

Step-by-step solution

( aligned & Let b+c 9 = c+a 10 = a+b 11 =k & b+c=9 k, c+a=10 k and a+b=11 k & and a+b+c=15 k & a=6 k, b=5 k and c=4 k & A+ B C = b^2+c^2-a^2 2 b c + a^2+c^2-b^2 2 a c a^2+b^2-c^2 2 a b & = 25+16-36 40 + 36+16-25 48 36+25-16 60 & = 5 40 + 27 48 45 60 & = 1 8 + 9 16 3 4 11 16 3 4 = 11 12 aligned ) Hence, option (3) is correct.

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