Which of these lengths could be the sides of a triangle?

1) 20, 7, 14
2) 12, 22, 8

How would I determine this?
When I tried it 1) 245=400
and 2) 208 = 484

Looking at your results, you were checking if the sides formed a right-angled triangle.

That is not what the question was.

It asked which sides would form a triangle.

Your answer will be based on the property that in any triangle the sum of two of the sides must be greater than the third side.
So add up any two sides. If that sum is less than the side you did not use, then there is no triangle possible.

Hint: one set will form a triangle, the other doesn't.