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MHT CET202525 Apr 2025Morning ShiftMathematicsProperties of TrianglesActual

If in triangle A B C , with usual notations A 2 C 2 = B 2 and 2 s is the perimeter of the triangle, then the value of s is

Options

  1. A2b
  2. Bb
  3. C4b
  4. Db 2

Correct answer

A. 2b

Step-by-step solution

Given: A 2 C 2 = B 2 Applying half-angle formulas for sine: A 2 = (s-b)(s-c) bc B 2 = (s-a)(s-c) ac C 2 = (s-a)(s-b) ab Substituting into the given relation: (s-b)(s-c) bc (s-a)(s-b) ab = (s-a)(s-c) ac Squaring both sides eliminates the radicals: (s-b)(s-c) bc (s-a)(s-b) ab = (s-a)(s-c) ac (s-a)(s-b)^2(s-c) ab^2c = (s-a)(s-c) ac Canceling the non-zero terms (s-a) , (s-c) , a , and c : (s-b)^2 b^2 = 1 Taking square roots and using b > 0 : |s-b| b = 1 |s-b| = b This yields two possibilities: s-b = b . The case s-b =

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