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AP EAMCET202317 May 2023Evening ShiftMathematicsProperties of TrianglesActual

In A B C , if a, b, c are 5,12 and 13 respectively, then b^2 2 C+c^2 2 B=

Options

  1. A60
  2. B120
  3. C180
  4. D90

Correct answer

B. 120

Step-by-step solution

Given: a=5, b=12, c=13 Thus, S = a+b+c 2 =15 = s( ~s - a )( s - b )( s - c ) = 15 10 3 2 =30 Now, b^2 2 C+c^2 2 B aligned & =b^2 2 C C+c^2 2 B B & =2 b^2 2 a b a^2+b^2-c^2 2 a b +2 c^2 2 a c a^2+c^2-b^2 2 a c & = 2 a^2 ( a ^2+b^2-c^2 )+ 2 a^2 ( a ^2+c^2-b^2 ) & = 2 a^2 (2 a^2 )=4 =4 30=120 aligned

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