If (a + b) : (b + c) : (c + a) = 3 : 4 : 5 and 3a – 4b + 2c = 48, then c is equal to

18

a + b = 3R, b + c = 4R, c + a = 5R

Adding all of above, we get:

2(a + b + c) = 12R

(a + b + c) = 6R      ...............(i)

b + c = 4R   ...........(ii)

(i) - (ii)

a = 2R, similarly b = 1R,  c = 3R

Now,

⇒ 3a – 4b + 2C = 48

⇒ (3 × 2R) –  (4 × 1R) +  (2 × 3R) = 48

⇒ 6R - 4R + 6R = 48

⇒ 8R = 48

⇒ 1R = 6

Here,

 c = 3R = 3 × 6 = 18