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MHT CET202619 April 2026Morning ShiftMathematicsProperties of TrianglesActual

In ABC , with usual notations, if the sides a , b and c are in the ratio 18 : 17 : 7 , then A 2 : B 2 : C 2 =

Options

  1. A4 : 3 : 14
  2. B14 : 4 : 3
  3. C3 : 4 : 14
  4. D4 : 14 : 3

Correct answer

C. 3 : 4 : 14

Step-by-step solution

Let the sides of the triangle be a = 18k , b = 17k , and c = 7k . The semi-perimeter s is given by: s = a+b+c 2 = 18k + 17k + 7k 2 = 21k Using the half-angle formula for cotangent: A 2 = s(s-a) (s-b)(s-c) = s(s-a) Similarly, B 2 = s(s-b) and C 2 = s(s-c) . Thus, the required ratio is: A 2 : B 2 : C 2 = (s-a) : (s-b) : (s-c) Substituting the values of s , a , b , and c : s-a = 21k - 18k = 3k s-b = 21k - 17k = 4k s-c = 21k - 7k = 14k Therefore, the ratio is: 3k : 4k : 14k = 3 : 4 : 14 Answer: 3 : 4 : 14

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