`a+b : b+c : c+a=4 : 7 :9`
Find `a:b:c=?`

Answer

To solve the problem \( a + b : b + c : c + a = 4 : 7 : 9 \) and find the ratio \( a : b : c \), we can follow these steps:

### Step 1: Set up the equations based on the given ratio
From the ratio \( a + b : b + c : c + a = 4 : 7 : 9 \), we can express the three sums as:
- \( a + b = 4k \) (for some constant \( k \))
- \( b + c = 7k \)
- \( c + a = 9k \)