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AP EAMCET201921 Apr 2019Morning ShiftMathematicsProperties of TrianglesActual

In a A B C , if 3 a=b+c , then B 2 C 2 =

Options

  1. A1
  2. B2
  3. C1 3
  4. D1 2

Correct answer

B. 2

Step-by-step solution

Let a, b, c are the sides of the A B C and s is the semi-perimeter s= a+b+c 2 Put the value of Eq. (i), we get s= a+3 a 2 = 4 a 2 =2 a Now, B 2 C 2 gathered = s(s-b) (s-a)(s-c) s(s-c) (s-a)(s-b) A 2 = s(s-a) (s-b)(s-c) gathered Put the value of s , we get aligned & = 2 a(2 a-b) (2 a-a)(2 a-c) 2 a(2 a-c) (2 a-a)(2 a-b) & = 2 a(2 a-b) a(2 a-c) 2 a(2 a-c) a(2 a-b) = 4 =2 aligned

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