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MHT CET202526 Apr 2025Morning ShiftMathematicsProperties of TrianglesActual

In a triangle A B C , with usual notations, (a+b+c)(a+b-c)=3 a b , then C =

Options

  1. A2
  2. B4
  3. C3
  4. D6

Correct answer

C. 3

Step-by-step solution

Given equation: (a+b+c)(a+b-c)=3ab . Applying the difference of squares identity, (a+b+c)(a+b-c)= (a+b)^2 - c^2 . Expanding and substituting gives a^2 + b^2 + 2ab - c^2 = 3ab , which simplifies to a^2 + b^2 - c^2 = ab . Using the Law of Cosines: a^2 + b^2 - c^2 = 2ab C , so we equate to get 2ab C = ab . Dividing both sides by ab (since a 0 and b 0 ) gives C = 1 2 , so C = 3 . Final answer: C

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