To determine if a triangle can be formed with these side lengths, we need to check if the sum of the lengths of any two sides is always greater than the length of the third side.
Let's check the first condition: 4.24 + 9.89 > 8.75
This becomes 14.13 > 8.75, which is true.
Now let's check the second condition: 4.24 + 8.75 > 9.89
This becomes 12.99 > 9.89, which is true.
Finally, let's check the third condition: 9.89 + 8.75 > 4.24
This becomes 18.64 > 4.24, which is true.
Since all three conditions are true, we can conclude that sides with lengths of 4.24 inches, 9.89 inches, and 8.75 inches can form a triangle.