There is a certain relationship between numbers on the left side of :: find out same relationship on the right side of :: ?

225 : 257 :: 289 : ?

325

The correct answer is Option 2: 325

First number ($225$): This is a perfect square of $15$.- $15^2 = 225$

Second number ($257$): This is obtained by taking the square of the next consecutive number ($16$) and adding $1$.- $(15 + 1)^2 + 1 = 16^2 + 1 = 256 + 1 = 257$

Apply the exact same relationship to the right side of the proportion ($289 : ?$)

Third number ($289$): This is a perfect square of $17$.- $17^2 = 289$

Fourth number ($?$): Take the square of the next consecutive number ($18$) and add $1$.$(17 + 1)^2 + 1 = 18^2 + 1 = 324 + 1 = 325$

Therefore, the missing number is 325.