Final answer:
The inequality for the range of the length of the third side of a triangle, given two side lengths of 10 and 16, is c < 26.
Step-by-step explanation:
To find an inequality for the range of the length of the third side of a triangle, we can use the triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Let's denote the two given side lengths as a = 10 and b = 16. The inequality for the range of the length of the third side, c, would be:
a + b > c
Substituting the given values, we have:
10 + 16 > c
26 > c
Therefore, the range for the length of the third side of the triangle is c < 26, meaning the third side must be less than 26 units.