Explanation:

- The problem involves finding a pattern of relationship between pairs of numbers.

- 12 : 225: The relationship is ${15}^2=225$, where 15 is derived from 12 + 3.

- 10 : 169: The relationship is ${13}^2=169$, where 13 is derived from 10 + 3.

- Therefore, the pattern involves adding 3 to the number and squaring the result.

- 14 : ?: Add 3 to 14, getting 17. Squaring 17 gives ${17}^2=289$.

- Option 1: 289 is calculated as shown.

- Option 2: 441 is ${21}^2$ and doesn't fit the pattern.

- Option 3: 361 is ${19}^2$ and doesn't fit the pattern.

- Option 4: 529 is ${23}^2$ and doesn't fit the pattern.

- The correct choice is Option 1: 289 .

.