Question

if (a+b) : (b+c) : (c+a) = 6:7:8 and a+b+c = 14 , then find a:b:c

Answer 1

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Answer 2

Answer:

(a+b):(b+c):(c+a)=6:7:8

(a+b+c)=14

a:b:c=?

a:b:c=14:10:18

Step-by-step explanation:

if we put x in  

(a+b)=6x-----(i)

(b+c)=7x-----(ii)

(c+a)=8x-----(iii)

Adding  (i)+(ii)+(iii)

when we open (a+b):(b+c):(c+a) it

a+b+b+c+c+a=6x+7x+8x

2(a+b+c)=21x

and we know (a+b+c)=14 so

2*14=21x

28/21=x

x=4/3

now we know x  

so  

(a+b+c)=14

c=14-(a+b)

c=14-6x              because (a+b)=6x

c=14-6*4/3        because x=4/3

c=14-8

c=6

a=14-(b+c)

a=14-7x              because (b+c)=7x

a=14-7*4/3        because x=4/3

a=14-28/3

a=42-28/3

a=14/3

b=14-(c+a)

b=14-8x              because (b+c)=8x

b=14-8*4/3        because x=4/3

b=14-32/3

b=42-32/3

b=10/3

a:b:c=14/3:10/3:6

when we take L.C.m those

take 3 *6=18=

so a:b:c=14:10:18