Explanation:

- To solve this problem, let's first understand the ratio (a + b) : (b + c) : (c + a) = 7 : 4 : 5.

- Assign variables k to these parts:

- a + b = 7k

- b + c = 4k

- c + a = 5k

- From these, calculate individual variables.

- Add the first two equations and subtract the third:

2b + 2a + 2c = 16k

- Use a + b + c = 16:

a + b + c = 8k = 16

- Find k = 2.

- Substitute back:

- a + b = 14, b + c = 8, c + a = 10.

- Calculate a, b, and c by solving these equations:

- a = 8, b = 6, c = 2.

- Square and product sums:

\((a^2 + b^2 + c^2) = 64 + 36 + 4 = 104\)

\((ab + bc + ca) = 48 + 12 + 16 = 76\)

- Ratio: (104 : 76) simplifies to 26:19.

Option 2 - 26:19 ?