Final answer:
The range for the length of the third side of a triangle with given side lengths of 22 and 15 is any value less than 37.
Step-by-step explanation:
The length of the third side of a triangle can be found using the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. So, for a triangle with sides of lengths a and b, the range for the length of the third side, c, can be represented by the inequality: a + b > c.
In the given case, if a = 22 and b = 15, then the inequality becomes: 22 + 15 > c, which simplifies to 37 > c. Therefore, the range for the length of the third side is any value less than 37.