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AP EAMCET2010MathematicsProperties of Triangles

If =a^2-(b-c)^2 , is the area of the A B C , then A is equal to

Options

  1. A1 16
  2. B8 15
  3. C3 4
  4. D4 3

Correct answer

B. 8 15

Step-by-step solution

=a^2-(b-c)^2 =(a+b-c)(a-b+c) =(2 s-c-c)(2 s-b-b)( 2 s=a+b+c) =(2 s-2 c)(2 s-2 b) =4(s-b)(s-c) = s(s-a)(s-b)(s-c) s(s-a)(s-b)(s-c) =4(s-b)(s-c) s(s-a) =4 (s-b)(s-c) 1 4 = (s-b)(s-c) s(s-a) A 2 = (s-b)(s-c) s(s-a) A 2 = 1 4 A= 2 A 2 1- ^2 A 2 = 2 1 4 1- 1 16 1 2 15 16 A= 8 15

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