Question

(a+b):(b+c):(c+a)=6:7:8 ho to a:b:c=?​

Answer 1

Answer:

good

Step-by-step explanation:

Answer 2

$\frac{ \frac{a + b}{b + c} }{c + a} = \frac{ \frac{6}{7} }{8} \\ \\ = > \frac{a + b}{b + c} = \frac{6}{7} \\ 7a + 7b = 6b + 6c \\ 7b - 6b = 6c - 7a \\ b = 6c - 7a \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ... \: (i)\\ \\ = > \frac{b + c}{c + a} = \frac{7}{8} \\ 8b + 8c = 7c + 7a \\ 8c - 7c = 7a - 8b \\ c = 7a - 8b \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ c = 7a - 8(6c - 7a) \: \: \: \: \: \: \: \: ... \: (from \: i) \\ c = 7a - 48c + 56a \\ c + 48c = 7a + 56a \\ 49c = 63a \\ \\ dividing \: throughout \: by \: 7 \\ \\ 7c = 9a \\ c = \frac{9}{7}a \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ... \: (ii)\\ \\ substituting \: in \: (i) \\ \\ b = 6( \frac{9}{7} a) - 7a \\ b = \frac{54}{7} a - 7a \\ \\ multiply \: throughout \: by \: 7 \\ \\ 7b = 54a - 49a \\ 7b = 5a \\ b = \frac{5}{7} a \\ \\ now \\ \frac{ \frac{a}{b} }{c} = \frac{ \frac{a}{ \frac{5}{7} a} }{ \frac{9}{7}a } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ... \: (from \: i \: and \: ii) \\ \\ mutiplying \: whole \: ratio \: with \: \frac{7}{a} \\ \frac{ \frac{a}{b} }{c} = \frac{ \frac{a \times \frac{7}{a} }{ \frac{5}{7}a \times \frac{7}{a} } }{ \frac{9}{7}a \times \frac{7}{a} } \\ \frac{ \frac{a}{b} }{c} = \frac{ \frac{7}{5} }{9}$

Hence,

a : b : c = 7 : 5 : 9