Given:
The two sides of a triangle are 2 and 6.
To find:
The side length that would NOT work to make a triangle with the two slide lengths of 2 and 6.
Solution:
For a triangle, the sum of two smaller sides must be greater than the largest side.
Let x be the third side.
Case 1: x is the largest side, then
...(i)
Case 2: x is not the largest side, then
...(ii)
From (i) and (ii), we get
Here, 4 and 8 are not included.
6, 5, 7 are included in the above interval, but 4 is not included in the above interval. It means 4 would NOT work to make a triangle with the two slide lengths of 2 and 6.
Therefore, the correct option is D.