The sum of squares of three positive integers is 323. If the sum of squares of two numbers is twice the third, their product is :

Answer: Option A

Let the integers in a, b, c
a² + b ² + c² = 323.....(i)
a² + b² + = 2c.....(ii)
Break the 323 in to their squares
a = 5
b = 3
c = 17
So, a² + b² + c² = 323
and
a² + b² = 2c
25² + 3² = 2 × 17
34 = 34
So, Satisfied
a : b : c = 17 × 5 × 3 = 255