In ABC , with usual notations, if b+c 11 = c+a 12 = a+b 13 , then the value of A + B + C is

Step-by-step solution

Let b + c 11 = c + a 12 = a + b 13 = k b+c=11 k ...(i) c+a=12 k ...(ii) and a+b=13 k ...(iii) From (i) +( ii) + (iii), 2(a+b+c)=36 k a+b+c=18 k ...(iv) Now, (iv) - (i) gives, a=7 k (iv) - (ii) gives, b=6 k (iv) - (iii) gives, c=5 k Now, aligned A & = b^2+c^2-a^2 2 b c & = (6 k)^2+(5 k)^2-(7 k)^2 2 (6 k) (5 k) & = 36 k^2+25 k^2-49 k^2 60 k^2 & = 12 k^2 60 k^2 & = 1 5 aligned aligned B & = c ^2+ a ^2- b ^2 2 ca & = (5 k )^2+(7 k )^2-(6 k )^2 2 (5 k ) (7 k ) & = 25 k ^2+49 k ^2-36 k ^2 70 k ^2 & = 38 k ^2 70 k ^2 & =