Select the option that is related to the third number in the same way as the second number is related to the first number.

13 : 196 :: 14 : ?

The correct answer is 225.

Step-by-step explanation:

We need to analyze the relationship between the first pair of numbers (13 : 196) and apply the exact same rule to find the missing number in the second pair (14 : ?).

Step 1: Determine the logic for the first pair (13 : 196).

Add 1 to the first number (13), which gives 14, and then square the result:

${(13+1)}^2={14}^2=196$

So the pattern is:

$\text{Second Number}={(\text{First Number}+1)}^2$

Step 2: Apply the pattern to the third number (14).

Add 1 to 14 and square the result:

${(14+1)}^2={15}^2=225$

Hence, the number related to 14 in the same way is 225.