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MHT CET202619 April 2026Evening ShiftMathematicsProperties of TrianglesActual

If ABC is a triangle of area with a = 2, b = 7 2 , c = 5 2 , where a, b, c are the lengths of the sides of the triangle opposite to angles A, B and C respectively, then 2 A - 2A 2 A + 2A is equal to...

Options

  1. A3 4
  2. B( 3 4 )^2
  3. C45 4
  4. D( 45 4 )^2

Correct answer

B. ( 3 4 )^2

Step-by-step solution

Simplifying the given expression: 2 A - 2A 2 A + 2A = 2 A(1 - A) 2 A(1 + A) 1 - A 1 + A = ^2 A 2 Using the half-angle formula in terms of the area : A 2 = (s-b)(s-c) Calculating the semi-perimeter s : s = a + b + c 2 = 2 + 7 2 + 5 2 2 = 4 Evaluating s-b and s-c : s - b = 4 - 7 2 = 1 2 s - c = 4 - 5 2 = 3 2 Substituting these values: A 2 = 1 2 3 2 = 3 4 Squaring both sides gives: ^2 A 2 = ( 3 4 )^2 Answer: ( 3 4 )^2

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