When a number is increased by 12, the results is equal to twice the number equation

Let the number be x

x + 12 = 2(x + 12)

x + 12 = 2x + 24

x - 2x = 24 - 12

-x = 12

x = -12

The number is -12.

I noticed a pattern:

Any side with an odd value followed by 2 consecutive numbers such as their sum is the square of the side will form a right triangle.

For instance:

3, 4, 5

3^2 = 4+5

Another one:

5, 12, 13

5^2 = 12+13

Check with Pythagorean Theorem:

a^2 + b^2 = c^2

3^2 + 4^2 = 5^2

9 + 16 = 25

5^2 + 12^2 = 13^2

25 + 144 = 169

Now we can apply that to these 3 options:

7, 25, 26

Check with Pattern: 7^2 25+26

Check with Pythagorean Theorem: 7^2 + 25^2 26^2

7, 23, 24

Check with Pattern: 7^2 23+24

Check with Pythagorean Theorem: 7^2 + 23^2 24^2

7, 24, 25

Check with Pattern: 7^2 = 24+25

Check with Pythagorean Theorem: 7^2 + 24^2 = 25^2

So that's our 7, 24, 25