Question

38. If (a+b) : (b+c) : (c+a) = 6:7:8 and a+b+c = 14 then the value of C

is​

Answer 1

Answer Key

$(a+b):(b+c):(c+a)=6:7:8$ is the ratio of the three numbers $a+b=6k$, $b+c=7k$, and $c+a=8k$.

Solution

Given,

$\implies a+b+c=14$

Adding the equations $a+b=6k$, $b+c=7k$, and $c+a=8k$,

$\implies 2(a+b+c)=21k$

$\implies a+b+c=\dfrac{21k}{2}$

Hence,

$\implies \dfrac{21k}{2} =14$

$\implies k=\dfrac{2}{21} \times 14$

$\implies \boxed{k=\dfrac{4}{3} }$

Hence,

$\implies a+b=8,\ b+c=\dfrac{28}{3} ,\ c+a=\dfrac{32}{3}$

Adding the last two equation gives

$\implies a+b+2c=20$

Subtracting the first equation gives

$\implies 2c=12$

$\implies \boxed{c=6}$

Answer 2

Answer:

Step-by-step explanation:

let the ratio be a+b,c+b , c+a = 6x,7x,8x

by adding all

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

2(a+b+c)=21x

a+b+c=21x/2

by equating

21x/2=14

x= 2/21x14

x=4/3

a+b=6 X 4/3

     = 8____(1)

a+b+c=14

8+c=14

c=14-8

c=6