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MHT CET202618 April 2026Morning ShiftMathematicsProperties of TrianglesActual

In ABC , with usual notation, if a = 13, b = 14, c = 15 , then the sum of the values of ( A 2 ) and A is....

Options

  1. A14 5 5
  2. B5 +4 5
  3. C5+ 5 5
  4. D2 5 + 1 2

Correct answer

B. 5 +4 5

Step-by-step solution

The semi-perimeter of the triangle is given by: s = a+b+c 2 = 13+14+15 2 = 21 Using Heron's formula, the area of the triangle is: = s(s-a)(s-b)(s-c) = 21 8 7 6 = 84 Using the area formula = 1 2 bc A , we get: A = 2 bc = 2 84 14 15 = 4 5 Using the half-angle formula for sine: ( A 2 ) = (s-b)(s-c) bc = 7 6 14 15 = 1 5 = 1 5 The required sum is: ( A 2 ) + A = 1 5 + 4 5 = 5 5 + 4 5 = 5 +4 5 Answer: 5 +4 5

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