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AP EAMCET201823 Apr 2018Evening ShiftMathematicsProperties of TrianglesActual

If s is the semi-perimeter of A B C and if s-a 4 = s-b 5 = s-c 6 , then ^2 ( A 2 )=

Options

  1. A74 25
  2. B25 74
  3. C74 33
  4. D25 33

Correct answer

D. 25 33

Step-by-step solution

Let s-a 4 = s-b 5 = s-c 6 =k b+c-a=8 k, a+c-b=10 k and a+b-c=12 k So, a+b+c=30 k s=15 k, a=11 k, b=10 k and c=9 k Now, aligned ^2 ( A 2 )= (s-b)(s-c) b c + (s-c)(s-a) c a & + & (s-a)(s-b) a b aligned aligned & = 30 k^2 90 k^2 + 24 k^2 99 k^2 + 20 k^2 110 k^2 & = 1 3 + 8 33 + 2 11 = 11+8+6 33 = 25 33 . aligned

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