Problem statement seems open ended.
A 5 meter long wire is cut into two pieces. If the longer piece is then used to form a perimeter of a square, what is the probability that the area of the square will be more than 1 if the original wire was cut at an arbitrary point?
I agree with the explanation given in the solution, but there can be infinite points in the first or the last 1 meter. I mean you can cut it at 0.1,0.11,0.2....similarly on the other side you can cut it at 4.1,4.11,4.12,4.13 etc. If I were the problem-setter I would put in a rider/statement that in someway restricts the number of favorable outcomes.