Explanation:

Let the two natural numbers be
n and n+1

Square of the sum of those numbers = (n + n + 1)^2 = (2n + 1)^2
Sum of their squares = n^2 + (n + 1)^2

Therefore from the given data we can incur that...

(2n + 1)^2 = n^2 + (n + 1)^2 + 112
4n^2 + 4n + 1 = n^2 + n^2 + 2n + 1 + 112

Rearrange the expression into a quadratic equation

2n^2 + 2n - 112 = 0
2n^2 + 16n - 14n - 112 = 0
2n (n + 8) - 14 (n + 8) = 0
(2n - 14)(n + 8) = 0

From this we can say n is 7 or -8, but since n is a natural number, it cannot be 8.
Hence, n is 7, n + 1 =8.

The numbers are 7 and 8

Hence, option 2 is the correct answer.