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MHT CET202520 Apr 2025Evening ShiftMathematicsProperties of TrianglesActual

In a triangle A B C with usual notations if a=13, b=14, c=15 Then A=

Options

  1. A4 5
  2. B3 5
  3. C1 2
  4. D4 7

Correct answer

A. 4 5

Step-by-step solution

Given triangle ABC with sides a=13 , b=14 , and c=15 , the semi-perimeter is s = 13+14+15 2 = 21 . Using Heron's formula, the area is K = s(s-a)(s-b)(s-c) = 21 8 7 6 = 7056 = 84 . The area can also be expressed as K = 1 2 bc A , so 84 = 1 2 14 15 A = 105 A . Solving yields A = 84 105 = 4 5 .

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