To get the solution, we test using the triangle inequality theorem
The triangle inequality theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side.
This means as soon as you know that the sum of 2 sides is less than (or equal to) the measure of a third side, then you know that the sides do not make up a triangle.
From the above theorem, the length of the third side that could not make a triangle is 13 feets because it does not follow the inequality theorem of a triangle.
4 + 7 < 13 and the sum must be greater than the third side.
Since the sum of 4 and 7 is less than 13, then 13 can not be the length of the third side.
Therefore, the answer is 13.