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

144 : 225 :: 169 : 256 :: ? : 361

256

Pattern followed is :

144 : 225

 (12 )² :  (12 + 3 )² = (12 )² :  (15)²

= 144 : 225

169 : 256

(13)² :  (13 + 3 )² = (13)² :  (16)²

= 169 : 256

Similarly ,

? : 361

(x )² :  (x + 3 )² = (x )² :  361

(x + 3 )² = 361

x+3 = 19

x = 16

(x )² = 256

256 is correct answer