If (a + b) : (b + c) : (c + a) = 3 : 8 : 7 and a + b + c = 27, then b…

(a + b) : (b + c) : (c + a) = 3 : 8 : 7 and a + b + c = 27

add all ratios:

⇒ a + b + b + c + c + a = (3 + 8 + 7)R

⇒ 2( a + b + c) = 18 R

⇒ a + b + c = 9R                             .............(i)

ATQ,

9R = 27

1R = 3

Now,

a + b + c = 9R              from (i)

c + a = 7R                   (given)

After subtraction, we get:

a + b + c - c - a = 9R - 7R

b = 2 R

∴ b = 2 × 3 = 6