In A B C , if r₁: r₂=7: 8 and r₁: r₃=3: 4 , then a: b: c=

Step-by-step solution

Given: r₁: r₂=7: 8 & r₁: r₃=3: 4 Now, r₁: r₂: r₃=7: 8: 28 / 3=21: 24: 28 aligned & s - a : s - b : s - c =21: 24: 28 & 1 ~s - a : 1 ~s - b : 1 ~s - c =21: 24: 28 aligned Let 1 s-a =21 k , 1 s-b =24 k , 1 s-c =28 k aligned & s - a = 1 21 k , s - b = 1 24 k , s - c = 1 28 k & 3 ~s -( a + b + c )= 1 21 k + 1 24 k + 1 28 k & 3 ~s -2 ~s = 1 8 k s = 1 8 k & a = 1 8 k - 1 21 k = 13 21 8 k , b = 1 8 k - 1 24 k = 2 24 k & c = 1 8 k - 1 28 k = 5 56 k aligned aligned & a: b: c= 13 21 8 k : 2 24 k : 5 56 k & a: b: c=13: 14: 15