Match the items of List-I with those of List-II (Here denotes the area of A B C .) Then the correct match is

Step-by-step solution

A= b^2+c^2-a^2 4 B= c^2+a^2-b^2 4 C= a^2+b^2-c^2 4 A= A+ B+ C= a^2+b^2+c^2 4 A 2 = s(s-a) , B 2 = s(s-b) and C 2 = s(s-c) A 2 = A 2 + B 2 + C 2 = s (s-a+s-b+s-c)= s (3 s-2 s)= s^2 = (a+b+c)^2 4 A: B: C=1: 2: 3 Let A=k, B=2 k, C=3 k A= k 1+k^2 , B= 2 k 1+4 k^2 , C= 3 k 1+4 k^2 A+B+C= A= A 6 k=6 k^3 k=1 A= 1 2 , B= 2 5 , C= 3 10 A: B: C= 5 : 2 2 : 3 A 2 : B 2 : C 2 =3: 7: 9 s(s-a) : s(s-b) : s(s-c) =3: 7: 9 s-a: s-b: s-c=3: 7: 9 s-a=3 k, s-b=7 k, s-c=9 k b+c-a=6 k, a+c-b=14 k, a+b-c=18 k Adding first two equations c=