Question

(x-a): (x-b):(x-c)=11:9:5, where x=(a+b+c)/2
What is the ratio of a,b,c​

Answer 1

Answer:

(s -- a) : (s -- b) : (s -- c) = 11 : 9 : 5 where

semi-perimeter s = (a + b + c)/2 then

(s -- a) : (s -- b) : (s -- c) = 11 : 9 : 5 gives

(s -- a)/11 = (s -- b)/9 = (s -- c)/5 = k, say then

(s -- a) = 11k, (s -- b) = 9k, (s -- c) = 5k

adding 3s -- (a + b + c) = 25k OR 3s -- 2s = 25k OR s = 25k giving

a = 14k, b = 16k, c = 20k

hence a : b : c = 14k : 16k : 20k = 7 : 8 : 10

Hope it helps you