Question

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

Answer 1

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Let (a+b) = 6x
(b+c) = 7x
(c+a) = 8x

2a + 2b + 2c = 21x
2 (a + b + c) = 21x
2 (14) = 21x

28 = 21x
x = 4/3
a+b = 6 * 4/3 = 8

a + b + c = 14
8 + c = 14
c = 6

b + 6 = 7 (4/3)
b = 28/3 - 18/3 = 10/3
b:c = (10/3)/(6/1) = 10/18 = 5/9

a + c = 8x
a + 6 = 32/3
a = 32/3 - 18/3 = 14/3
a:c = (14/3)/(6/1) = 14/18 = 7/9

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