In a triangle ABC, with usual notations if s-a 11 = s-b 12 = s-c 13 and ^2 A 2 = 455 , then =

Step-by-step solution

Let s-a 11 = s-b 12 = s-c 13 = k s-a = 11k , s-b = 12k , s-c = 13k Adding these three equations, we get: 3s - (a+b+c) = 11k + 12k + 13k Since a+b+c = 2s , this becomes: 3s - 2s = 36k s = 36k Using the half-angle formula for tangents: ^2 A 2 = (s-b)(s-c) s(s-a) Substituting the values in terms of k : ^2 A 2 = 12k 13k 36k 11k = 12 13 36 11 = 13 33 Given that ^2 A 2 = 455 : 13 33 = 455 = 455 33 13 = 35 33 = 1155 Answer: 1155