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AP EAMCET201922 Apr 2019Morning ShiftMathematicsProperties of TrianglesActual

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

Options

  1. A1
  2. B( 13 15 )
  3. C( 1 4 )
  4. D( 8 15 )

Correct answer

D. ( 8 15 )

Step-by-step solution

Given, ( aligned & Area of a triangle =b^2-(c-a)^2 & =b^2-(c-a)^2 & =(b+c-a)(b-c+a) & =(2 s-2 a)(2 s-2 c) & =4(s-a)(s-c) aligned ) Now ( s(s-a)(s-b)(s-c) =4(s-a)(s-c) ) ( aligned & s(s-b) =4 (s-a)(s-c) & 1 4 = (s-a)(s-c) s(s-b) 1 4 = ( B 2 ) & B= 2 ( B 2 ) 1- ^2 ( B 2 ) = 2 1 4 1- 1 16 = 1 2 15 16 & = 1 2 16 15 = 8 15 aligned )

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